diff --git a/dvc/command/run.py b/dvc/command/run.py
--- a/dvc/command/run.py
+++ b/dvc/command/run.py
@@ -2,6 +2,7 @@
 import logging
 
 from dvc.command.base import CmdBase, append_doc_link
+from dvc.command.stage import parse_cmd
 from dvc.exceptions import DvcException
 
 logger = logging.getLogger(__name__)
@@ -22,7 +23,7 @@ def run(self):
                 self.args.outs_persist_no_cache,
                 self.args.checkpoints,
                 self.args.params,
-                self.args.command,
+                self.args.cmd,
             ]
         ):  # pragma: no cover
             logger.error(
@@ -34,7 +35,7 @@ def run(self):
 
         try:
             self.repo.run(
-                cmd=self._parsed_cmd(),
+                cmd=parse_cmd(self.args.cmd),
                 outs=self.args.outs,
                 outs_no_cache=self.args.outs_no_cache,
                 metrics=self.args.metrics,
@@ -67,27 +68,6 @@ def run(self):
 
         return 0
 
-    def _parsed_cmd(self):
-        """
-        We need to take into account two cases:
-
-        - ['python code.py foo bar']: Used mainly with dvc as a library
-        - ['echo', 'foo bar']: List of arguments received from the CLI
-
-        The second case would need quoting, as it was passed through:
-                dvc run echo "foo bar"
-        """
-        if len(self.args.command) < 2:
-            return " ".join(self.args.command)
-
-        return " ".join(self._quote_argument(arg) for arg in self.args.command)
-
-    def _quote_argument(self, argument):
-        if " " not in argument or '"' in argument:
-            return argument
-
-        return f'"{argument}"'
-
 
 def add_parser(subparsers, parent_parser):
     from dvc.command.stage import _add_common_args
@@ -103,7 +83,6 @@ def add_parser(subparsers, parent_parser):
     run_parser.add_argument(
         "-n", "--name", help="Stage name.",
     )
-    _add_common_args(run_parser)
     run_parser.add_argument(
         "--file", metavar="<filename>", help=argparse.SUPPRESS,
     )
@@ -134,7 +113,5 @@ def add_parser(subparsers, parent_parser):
         default=False,
         help=argparse.SUPPRESS,
     )
-    run_parser.add_argument(
-        "command", nargs=argparse.REMAINDER, help="Command to execute."
-    )
+    _add_common_args(run_parser)
     run_parser.set_defaults(func=CmdRun)
diff --git a/dvc/command/stage.py b/dvc/command/stage.py
--- a/dvc/command/stage.py
+++ b/dvc/command/stage.py
@@ -105,10 +105,32 @@ def log_error(relpath: str, exc: Exception):
         return 0
 
 
+def parse_cmd(commands: List[str]) -> str:
+    """
+    We need to take into account two cases:
+
+    - ['python code.py foo bar']: Used mainly with dvc as a library
+    - ['echo', 'foo bar']: List of arguments received from the CLI
+
+    The second case would need quoting, as it was passed through:
+            dvc run echo "foo bar"
+    """
+
+    def quote_argument(arg: str):
+        should_quote = " " in arg and '"' not in arg
+        return f'"{arg}"' if should_quote else arg
+
+    if len(commands) < 2:
+        return " ".join(commands)
+    return " ".join(map(quote_argument, commands))
+
+
 class CmdStageAdd(CmdBase):
     def run(self):
         repo = self.repo
         kwargs = vars(self.args)
+        kwargs["cmd"] = parse_cmd(kwargs.pop("cmd"))
+
         stage = repo.stage.create_from_cli(validate=True, **kwargs)
 
         with repo.scm.track_file_changes(config=repo.config):
@@ -226,7 +248,7 @@ def _add_common_args(parser):
         metavar="<filename>",
     )
     parser.add_argument(
-        "-C",
+        "-c",
         "--checkpoints",
         action="append",
         default=[],
@@ -254,6 +276,12 @@ def _add_common_args(parser):
             "This doesn't affect any DVC operations."
         ),
     )
+    parser.add_argument(
+        "cmd",
+        nargs=argparse.REMAINDER,
+        help="Command to execute.",
+        metavar="command",
+    )
 
 
 def add_parser(subparsers, parent_parser):
@@ -282,15 +310,8 @@ def add_parser(subparsers, parent_parser):
         help=STAGE_ADD_HELP,
         formatter_class=argparse.RawDescriptionHelpFormatter,
     )
-    stage_add_parser.add_argument("name", help="Name of the stage to add")
     stage_add_parser.add_argument(
-        "-c",
-        "--command",
-        action="append",
-        default=[],
-        dest="cmd",
-        help="Command to execute.",
-        required=True,
+        "-n", "--name", help="Name of the stage to add", required=True
     )
     _add_common_args(stage_add_parser)
     stage_add_parser.set_defaults(func=CmdStageAdd)

I don't understand the autocompletion issue with the `-c "echo bar > bar"` format. I'm able to autocomplete on Ubuntu in bash and zsh even inside of quotes. Is there an example of how this breaks autocompletion? Is it a specific issue with OSX? Maybe @dmpetrov can elaborate?
@dberenbaum, that's strange. For me (on Linux), it never autocompletes, with or without DVC's autocompletion.
@skshetry What are you trying to autocomplete? What shell are you using? Does autocomplete work for you without the `-c` flag and quotes?
@dberenbaum Autocompletion issue - the default autocomplete suggests files that I have in a dir when I type `dvc run -n s1 python tr<TAB>` (suggests `train.py`). It won't suggest inside a quoted string - `dvc run s1 -c " python tr<TAB>` (however, it suggests as 1st item in a string `dvc run s1 -c "tr<TAB>` which is not a usual corner case).

@skshetry The decision about string VS reminder was made in the very first version of DVC. I considered a `-c/--command` option as the opposite of the remainder. The reminder looks more common and convenient. An analogy with a reminder - `xargs`.

To my mind, the issue with mixing up params is not a major one. By replacing the behavior we might have new issues (the autocomplete is one of them). I suggest not changing the behavior and keep cmd as a reminder.
Thanks, @dmpetrov! I was trying the equivalent of `dvc run s1 -c "tr<TAB>`, but now I understand and see the same on my end.
I agree that `But, we have heard complaints from users that it's confusing, as trying to add certain flags to dvc run at the end is now assumed to be part of the user's script.` doesn't sound like a big issue, considering that people will have to double quote commands now (and escaping if needed) + they will have to remember/learn about `-c` + it breaks autocompletion (not matter DVC's one installed or not).
Yup, let's stick with the existing syntax (positional arguments) unless you have any concerns @skshetry .
diff --git a/tests/func/test_cli.py b/tests/func/test_cli.py
--- a/tests/func/test_cli.py
+++ b/tests/func/test_cli.py
@@ -66,7 +66,7 @@ def test(self):
         self.assertEqual(args.outs, [out1, out2])
         self.assertEqual(args.outs_no_cache, [out_no_cache1, out_no_cache2])
         self.assertEqual(args.file, fname)
-        self.assertEqual(args.command, [cmd, arg1, arg2])
+        self.assertEqual(args.cmd, [cmd, arg1, arg2])
 
 
 class TestPull(TestDvc):
diff --git a/tests/unit/command/test_stage.py b/tests/unit/command/test_stage.py
--- a/tests/unit/command/test_stage.py
+++ b/tests/unit/command/test_stage.py
@@ -5,17 +5,19 @@
 
 
 @pytest.mark.parametrize(
-    "extra_args, expected_extra",
+    "command, parsed_command",
     [
-        (["-c", "cmd1", "-c", "cmd2"], {"cmd": ["cmd1", "cmd2"]}),
-        (["-c", "cmd1"], {"cmd": ["cmd1"]}),
+        (["echo", "foo", "bar"], "echo foo bar"),
+        (["echo", '"foo bar"'], 'echo "foo bar"'),
+        (["echo", "foo bar"], 'echo "foo bar"'),
     ],
 )
-def test_stage_add(mocker, dvc, extra_args, expected_extra):
+def test_stage_add(mocker, dvc, command, parsed_command):
     cli_args = parse_args(
         [
             "stage",
             "add",
+            "--name",
             "name",
             "--deps",
             "deps",
@@ -53,7 +55,7 @@ def test_stage_add(mocker, dvc, extra_args, expected_extra):
             "--desc",
             "description",
             "--force",
-            *extra_args,
+            *command,
         ]
     )
     assert cli_args.func == CmdStageAdd
@@ -62,27 +64,32 @@ def test_stage_add(mocker, dvc, extra_args, expected_extra):
     m = mocker.patch.object(cmd.repo.stage, "create_from_cli")
 
     assert cmd.run() == 0
-    expected = dict(
-        name="name",
-        deps=["deps"],
-        outs=["outs"],
-        outs_no_cache=["outs-no-cache"],
-        params=["file:param1,param2", "param3"],
-        metrics=["metrics"],
-        metrics_no_cache=["metrics-no-cache"],
-        plots=["plots"],
-        plots_no_cache=["plots-no-cache"],
-        live="live",
-        live_no_summary=True,
-        live_no_report=True,
-        wdir="wdir",
-        outs_persist=["outs-persist"],
-        outs_persist_no_cache=["outs-persist-no-cache"],
-        checkpoints=["checkpoints"],
-        always_changed=True,
-        external=True,
-        desc="description",
-        **expected_extra
-    )
-    # expected values should be a subset of what's in the call args list
-    assert expected.items() <= m.call_args[1].items()
+    expected = {
+        "name": "name",
+        "deps": ["deps"],
+        "outs": ["outs"],
+        "outs_no_cache": ["outs-no-cache"],
+        "params": ["file:param1,param2", "param3"],
+        "metrics": ["metrics"],
+        "metrics_no_cache": ["metrics-no-cache"],
+        "plots": ["plots"],
+        "plots_no_cache": ["plots-no-cache"],
+        "live": "live",
+        "live_no_summary": True,
+        "live_no_report": True,
+        "wdir": "wdir",
+        "outs_persist": ["outs-persist"],
+        "outs_persist_no_cache": ["outs-persist-no-cache"],
+        "checkpoints": ["checkpoints"],
+        "always_changed": True,
+        "external": True,
+        "desc": "description",
+        "cmd": parsed_command,
+    }
+    args, kwargs = m.call_args
+    assert not args
+
+    for key, val in expected.items():
+        # expected values should be a subset of what's in the call args list
+        assert key in kwargs
+        assert kwargs[key] == val

stage:add: decide on `-c` command vs remainder arg for user's script
On `dvc run`, the remainder positional argument is considered as a script. 
```console
$ dvc run -n stage_name -o bar -w data echo bar > bar
```

But, we have heard complaints from users that it's confusing, as trying to add certain flags to `dvc run` at the end is now assumed to be part of the user's script. 

So, on `stage:add`, we moved it under the `-c`/`--command` flag and now needs to be explicitly specified and quoted.
```console
$ dvc stage add stage_name -o bar -w data -c "echo bar > bar"
```

@dmpetrov later pointed out that it breaks the autocompletion for users. This discussion was without any DVC's autocompletion installed.

With DVC's autocompletion installed, the autocompletion anyway does not work as it is assumed as a plain string.

Anyway, we have to either choose between`-c` and the remainder arg in `run`.

cc @dberenbaum @shcheklein @jorgeorpinel 


tests/func/test_cli.py::TestRun::test tests/unit/command/test_stage.py::test_stage_add[command0-echo tests/unit/command/test_stage.py::test_stage_add[command1-echo tests/unit/command/test_stage.py::test_stage_add[command2-echo
tests/func/test_cli.py::TestArgParse::test tests/func/test_cli.py::TestPull::test tests/func/test_cli.py::TestPush::test tests/func/test_cli.py::TestStatus::test tests/func/test_cli.py::TestRepro::test tests/func/test_cli.py::TestRemove::test tests/func/test_cli.py::TestAdd::test tests/func/test_cli.py::TestGC::test tests/func/test_cli.py::TestGCMultipleDvcRepos::test tests/func/test_cli.py::TestConfig::test tests/func/test_cli.py::TestConfig::test_config_list tests/func/test_cli.py::TestCheckout::test tests/func/test_cli.py::TestFindRoot::test tests/func/test_cli.py::TestCd::test tests/func/test_cli.py::test_unknown_command_help tests/func/test_cli.py::test_unknown_subcommand_help