My name isn't correct in my iPhone?

Okay so about a month ago me and my brother got iPhone 4S's. We had our numbers transferred from our old phones to the iPhones. We got them in the mail, got them registered and set up and everything. I recently got a Snapchat, and a friend asked me why my Snapchat name was my brother's name.

(I'm gonna use example names. I'll be John Smith and my brother will be Mike Smith.)

I looked on his Snapchat and sure enough, I'm Mike Smith on Snapchat. I checked to see if this was occurring anywhere else and it is over a few things. It's really annoying that I pop up as my brother's name everywhere. So if anyone can help me out with this I'd really appreciate it.

You need separate Apple ID's.

Change your itunes user ID