Q: Same Apple ID on two phones- How to get a new ID on one of them?

Log out of iCloud, App Store, and iMessage / FaceTime on the second phone. Create a new account, then log in on that second phone with that account.

Having two separate Apple IDs would (and should) make the iPhones behave as if two different folks own them.

I suggest doing a thorough job of clearing the one iPhone before you change its Apple ID.  This will avoid confusion; for example, Apple ID #1 does not own the apps or music that Apple ID #2 owns.

Clear out completely the iPhone you are changing, just as if you were selling it.

What to do before selling or giving away your iPhone, iPad, or iPod touch - Apple Support