This is a cool little hint I read about online. If you would like to rename any of your Pokemon you have to first go to the Monster page from your menu. After that just click on the grey pencil next to the name and chose what you would like! I am not sure if you can rename them, I haven't tried yet. So in case you can't... Be 100% certain of the name you choose!
I don't think you can rename them either. I was naming a Pidgey I caught the other day "Puddles" because I found him in a puddle lol and I go to enter the name and my phone derp'd on me and spelled it out "Poodles" for some reason so yeah... Needless to stay, I have a Pokemon bird type named after a dog breed. lol
I didn't know about this! COOL! I was wondering if we could name them like on the DS games. I am happy they allowed this. I always think of such funny names with in minuted of me catching them too!