I try to name my pets, but its not letting me name. any soultions?

It most likely means that name is already taken, so get creative with them!

yep, names are unique on Rescreatu which means a name can only be used once. 
Fore example there can only be one creatu called Bob.

You'll know is a name is free when the nameing box and font turn green, if it's red the name is taken, too long or has "extra characters (such as a space or a full stop)

good luck :D