It is currently not possible to remove the CustomName NBT tag from any entity. Trying it will result in the command succeeding but the NBT tag will be unchanged. It is also not possible to set the CustomName to an empty string.
How to replicate:
Summon an entity with a CustomName.
Make sure you can see the Name above the entity so you know it actually has the CustomName NBT tag.
Run a data get command that returns the CustomName NBT tag.
Remove the CustomName NBT tag.
Run the data get command again.
You will see that the CustomName has not changed.