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Yes, exactly, you don't use is for equality comparison. It tests object identity, which is why it makes sense to use it with a sentinel.
The 'name' of the sentinel is purely a way to store and retrieve particular sentinel objects. The sentinel itself does not have a name.
Good point about copy...the copy protocol and the pickle protocol are closely related, so preventing a sentinel from being pickled may prevent it from being copied as well. It is an interesting question how surprising people will find it for a sentinel to throw an error if an attempt is made to copy it, but if the test is using a sentinel, presumably it expects the sentinel to survive unchanged, so an error on copy is probably a reasonable result. You could imagine someone wanting to use a sentinel to test that copy happens by making sure they get back a different object, though, so it is not entirely clear cut. However, I expect that to be *much* less common than wanting to use it to prove that an object is preserved (not copied).