Here goes:
First, you need to create a new Apple ID...must be a verified email address. Next, make sure your contacts, calendars & iTunes content are on your computer...remember, we're going "nuclear"...you're gonna lose ALL data on your phone...messages...app data...everything. You won't be restoring from backup. Then, on your phone: turn off FaceTime, iMessage & delete the iCloud account...settings>iCloud>scroll down>delete account. Then: Settings>General>Reset>Erase All Content & Settings. When you go to reactivate/setup again, select "new" device, & use your new Apple for iCloud. Once setup, you can activate FaceTime, but do not turn iMessage on or activate it. Go into Settings>iTunes/App store & use your old ID...if your new ID is shown, tap it, sign out, then sign back in with your old ID. Now, connect to iTunes & sync your contacts & iTunes content back to the phone.
That should do it.
Make a full backup before you proceed in case you change your mind or want to go back.