diff --git a/dvc/repo/experiments/__init__.py b/dvc/repo/experiments/__init__.py
--- a/dvc/repo/experiments/__init__.py
+++ b/dvc/repo/experiments/__init__.py
@@ -473,6 +473,17 @@ def _log_reproduced(self, revs: Iterable[str], tmp_dir: bool = False):
             "\tdvc exp branch <exp> <branch>\n"
         )
 
+    def _validate_new_ref(self, exp_ref: ExpRefInfo):
+        from .utils import check_ref_format
+
+        if not exp_ref.name:
+            return
+
+        check_ref_format(self.scm, exp_ref)
+
+        if self.scm.get_ref(str(exp_ref)):
+            raise ExperimentExistsError(exp_ref.name)
+
     @scm_locked
     def new(self, *args, checkpoint_resume: Optional[str] = None, **kwargs):
         """Create a new experiment.
@@ -485,6 +496,16 @@ def new(self, *args, checkpoint_resume: Optional[str] = None, **kwargs):
                 *args, resume_rev=checkpoint_resume, **kwargs
             )
 
+        name = kwargs.get("name", None)
+        baseline_sha = kwargs.get("baseline_rev") or self.repo.scm.get_rev()
+        exp_ref = ExpRefInfo(baseline_sha=baseline_sha, name=name)
+
+        try:
+            self._validate_new_ref(exp_ref)
+        except ExperimentExistsError as err:
+            if not (kwargs.get("force", False) or kwargs.get("reset", False)):
+                raise err
+
         return self._stash_exp(*args, **kwargs)
 
     def _resume_checkpoint(
diff --git a/dvc/repo/experiments/utils.py b/dvc/repo/experiments/utils.py
--- a/dvc/repo/experiments/utils.py
+++ b/dvc/repo/experiments/utils.py
@@ -157,3 +157,12 @@ def resolve_exp_ref(
         msg.extend([f"\t{info}" for info in exp_ref_list])
         raise InvalidArgumentError("\n".join(msg))
     return exp_ref_list[0]
+
+
+def check_ref_format(scm: "Git", ref: ExpRefInfo):
+    # "/" forbidden, only in dvc exp as we didn't support it for now.
+    if not scm.check_ref_format(str(ref)) or "/" in ref.name:
+        raise InvalidArgumentError(
+            f"Invalid exp name {ref.name}, the exp name must follow rules in "
+            "https://git-scm.com/docs/git-check-ref-format"
+        )
diff --git a/dvc/scm/git/__init__.py b/dvc/scm/git/__init__.py
--- a/dvc/scm/git/__init__.py
+++ b/dvc/scm/git/__init__.py
@@ -346,6 +346,7 @@ def get_fs(self, rev: str):
     status = partialmethod(_backend_func, "status")
     merge = partialmethod(_backend_func, "merge")
     validate_git_remote = partialmethod(_backend_func, "validate_git_remote")
+    check_ref_format = partialmethod(_backend_func, "check_ref_format")
 
     def resolve_rev(self, rev: str) -> str:
         from dvc.repo.experiments.utils import exp_refs_by_name
diff --git a/dvc/scm/git/backend/dulwich/__init__.py b/dvc/scm/git/backend/dulwich/__init__.py
--- a/dvc/scm/git/backend/dulwich/__init__.py
+++ b/dvc/scm/git/backend/dulwich/__init__.py
@@ -681,3 +681,8 @@ def validate_git_remote(self, url: str, **kwargs):
             os.path.join("", path)
         ):
             raise InvalidRemoteSCMRepo(url)
+
+    def check_ref_format(self, refname: str):
+        from dulwich.refs import check_ref_format
+
+        return check_ref_format(refname.encode())

For reference, the intended behavior is:

> dvc exp run should refuse to assign names with white space in them,

Experiment names must be valid Git ref/branch names and cannot contain whitespace (https://git-scm.com/docs/git-check-ref-format)
diff --git a/tests/func/experiments/test_experiments.py b/tests/func/experiments/test_experiments.py
--- a/tests/func/experiments/test_experiments.py
+++ b/tests/func/experiments/test_experiments.py
@@ -53,6 +53,7 @@ def test_experiment_exists(tmp_dir, scm, dvc, exp_stage, mocker, workspace):
         tmp_dir=not workspace,
     )
 
+    new_mock = mocker.spy(dvc.experiments, "_stash_exp")
     with pytest.raises(ExperimentExistsError):
         dvc.experiments.run(
             exp_stage.addressing,
@@ -60,6 +61,7 @@ def test_experiment_exists(tmp_dir, scm, dvc, exp_stage, mocker, workspace):
             params=["foo=3"],
             tmp_dir=not workspace,
         )
+    new_mock.assert_not_called()
 
     results = dvc.experiments.run(
         exp_stage.addressing,
@@ -685,3 +687,16 @@ def test_exp_run_recursive(tmp_dir, scm, dvc, run_copy_metrics):
     )
     assert dvc.experiments.run(".", recursive=True)
     assert (tmp_dir / "metric.json").parse() == {"foo": 1}
+
+
+def test_experiment_name_invalid(tmp_dir, scm, dvc, exp_stage, mocker):
+    from dvc.exceptions import InvalidArgumentError
+
+    new_mock = mocker.spy(dvc.experiments, "_stash_exp")
+    with pytest.raises(InvalidArgumentError):
+        dvc.experiments.run(
+            exp_stage.addressing,
+            name="fo^o",
+            params=["foo=3"],
+        )
+    new_mock.assert_not_called()
diff --git a/tests/unit/repo/experiments/test_utils.py b/tests/unit/repo/experiments/test_utils.py
--- a/tests/unit/repo/experiments/test_utils.py
+++ b/tests/unit/repo/experiments/test_utils.py
@@ -1,7 +1,8 @@
 import pytest
 
+from dvc.exceptions import InvalidArgumentError
 from dvc.repo.experiments.base import EXPS_NAMESPACE, ExpRefInfo
-from dvc.repo.experiments.utils import resolve_exp_ref
+from dvc.repo.experiments.utils import check_ref_format, resolve_exp_ref
 
 
 def commit_exp_ref(tmp_dir, scm, file="foo", contents="foo", name="foo"):
@@ -25,3 +26,16 @@ def test_resolve_exp_ref(tmp_dir, scm, git_upstream, name_only, use_url):
     remote_ref_info = resolve_exp_ref(scm, "foo" if name_only else ref, remote)
     assert isinstance(remote_ref_info, ExpRefInfo)
     assert str(remote_ref_info) == ref
+
+
+@pytest.mark.parametrize(
+    "name,result", [("name", True), ("group/name", False), ("na me", False)]
+)
+def test_run_check_ref_format(scm, name, result):
+
+    ref = ExpRefInfo("abc123", name)
+    if result:
+        check_ref_format(scm, ref)
+    else:
+        with pytest.raises(InvalidArgumentError):
+            check_ref_format(scm, ref)

exp run: Results cannot be found if experiment name includes space
# Bug Report

## Description 
When running an experiment with white space in the name, the resulting experiment does not show up in `exp show` later.

### Reproduce

1. `dvc exp run --name "some name": Experiments runs as expected.
2. `dvc exp show`: Experiment is not listed.

### Expected

I would expect that either

- `dvc exp run` should refuse to assign names with white space in them,
- or `dvc exp show` shows this experiment in the summary regardless of the white space in the name.

### Environment information

**Output of `dvc doctor`:**

```console
DVC version: 2.7.2 (pip)
---------------------------------
Platform: Python 3.7.10 on Linux-5.14.5-arch1-1-x86_64-with-arch
```

tests/func/experiments/test_experiments.py::test_no_scm tests/func/experiments/test_experiments.py::test_run_metrics tests/func/experiments/test_experiments.py::test_fix_exp_head[] tests/func/experiments/test_experiments.py::test_fix_exp_head[~1] tests/func/experiments/test_experiments.py::test_fix_exp_head[^] tests/func/experiments/test_experiments.py::test_experiment_name_invalid tests/unit/repo/experiments/test_utils.py::test_resolve_exp_ref[True-True] tests/unit/repo/experiments/test_utils.py::test_resolve_exp_ref[True-False] tests/unit/repo/experiments/test_utils.py::test_resolve_exp_ref[False-True] tests/unit/repo/experiments/test_utils.py::test_resolve_exp_ref[False-False] tests/unit/repo/experiments/test_utils.py::test_run_check_ref_format[name-True] tests/unit/repo/experiments/test_utils.py::test_run_check_ref_format[group/name-False] tests/unit/repo/experiments/test_utils.py::test_run_check_ref_format[na