You can wipe the iPhone and start over:
You can sign out of your Apple ID from all services:
Settings->iTunes & App Stores->Apple ID
Settings->Account(top of settings)->Scroll Down to "Sign Out" for iCloud.
Settings->Messages->Send & Receive->Apple ID
Then you can go to any of those locations and Select Create new Apple ID in the Sign in Menu.
Note that doing with will not delete any content, and any Apps downloaded with your other Apple ID will remain tied to it, and require it to update.