Minecraft wiki entry for Name_Tag, associated text: Any mob that receives the name "Dinnerbone" or "Grumm" is rendered upside down. This even includes the player in early versions of Bedrock Edition if the username is set to either of these and you are not signed into Xbox Live.
Naming a sheep "jeb_" causes its wool to fade between the dye colors, producing a rainbow effect. The wool that drops when the sheep is sheared or killed is the original color of the sheep before the sheep was named.
Naming a rabbit "Toast" causes it to have a special memorial skin of user xyzen420's girlfriend's missing rabbit.
Naming a vindicator "Johnny" causes it to be aggressive and attack all mobs including the wither (except ghasts and other illagers). The hostility even extends to ravagers in Java Edition, as the "Johnny" vindicator can also attack the ravager while it's riding it.