Name is pretty self-explanatory but I'll explain anyways.

If I have an enchanted collar named 'Rio', and an unenchanted collar also named 'Rio', if I put one of them on a pet and then try to swap it for the other, it will not do anything.

Once I swapped out the enchanted collar for a blank one, the pet kept their name, but the tag didn't. While this makes sense, I feel like it should be explained on the mod page maybe.