How to change the apple ID on my iphone?

I changed it under store, but when I can't change it under icloud.
The phone was a gift from my boyfriend at the time, and it has his email.

Added (1). What would happen if I hit 'delete account' Would it just delete his icloud account off my phone, or would it mess up his account?

Go to settings and you can choose to change it on everythign