You can rename your pets (Mutts, Hermit Crab and the Cockroach) by targeting your pet and typing in /renamepet NAME or /renamemount NAME. You can also right click on the Status Bar of your mount, where the name is, which will bring up the Change Name option, click that and then change the name to one you like and then click OK to save.
All names of pets must follow the naming guidelines and no name can be given to a pet that is already used by a player.
Below is a list of the errors and the solutions to the errors that you may receive while attempting to rename your pet.
<GAME>: Petname is not a valid name
If you get this error, this means that the name does not meet our naming guidelines. Please view the Naming Guidelines here if you have any questions about the names that are allowed.
<GAME>: Queuing rename of Wasteland Mutt to petname Rename failed.
If you get this error, this means that the name has already been taken, please try a different name.
<GAME>: Failed to find mountname
If you get this error, this means that you have not selected your pet before running the command.
<GAME>: YourCharacterName may not be renamed
If you get this error, this means that you have yourself selected and not your pet.