Baumbart
Legend
Just to add to the thread... I did some testing some time ago with a DK and a f2p level 20 on a separate account.
Level 20 could see DK's custom pet name, DK couldn't see level 20's custom pet name (it just showed the default name). There seems to be a level-difference limit for pet names like there is for /s, so don't just stand there with your pet waiting for a whisper. The higher level can only see the pet's name when you point (or use any other emote) at the pet.
Also companion pet names aren't unique. You must have chosen a forbidden name if the system didn't allow you to change it.
Level 20 could see DK's custom pet name, DK couldn't see level 20's custom pet name (it just showed the default name). There seems to be a level-difference limit for pet names like there is for /s, so don't just stand there with your pet waiting for a whisper. The higher level can only see the pet's name when you point (or use any other emote) at the pet.
Also companion pet names aren't unique. You must have chosen a forbidden name if the system didn't allow you to change it.