Pick a letter then go to the baby names sites & check what names start with that letter. I had many toy poodles over the years (at least 13) & all of them had names that started with "S". My parrots are all "J" names.
You don't even have to name it right away, wait and see if an appropriate name pops up over the course of your relationship! Our African Grey is called Astro but we usually call him beep-beep because that's the sound he likes to make.