hi my pet name is "Improved Baby Kookaburra" as it would be not defined, but on item in inventory it say "name exist" and i can try change name on summoned pet i try do that it says name already exists (i am in town) if i try use 1 gold to erase name it says "pet name is not defined" so what to do ?

Pet names and character names have a common list. So you can't give a pet a name that some character has.
So just pick a pet name that is not occupied.