Now, I mostly played this game as an 11 and 12 year old, and i mean, wow, I did not realise i was ever THIS bad at naming things. Suffice to say I'd like to rename some creatu if that's at all possible because some of the names in my showroom are beyond atrocious. 

This may be a pretty obvious question but I haven't really touched this game in a decade so I have very little recollection of how it works.

Another option is to let pets die (which can take a long time) by keeping them on your profile and not feeding them and they will lose their name after some time in the Graveyard. (Alternatively you could use Potions of Death to send them to the Graveyard but it'll still take time for them to lose their names).