Iphone 5s phone contact is an email Recently I bought the iphone 5s and I am under my boyfriends icloud account. today I shut my phone off and turned it back on and when he texted me is icloud email showed up. when I text his phone number he gets it but when he replies it comes back under the email.

How do I fix this problem?
On HIS iPhone go to Settings > Messages > Send and Receive > Start New Conversations From and change the default to the entry for his phone number.

Also you didn't ask, but for what it's worth, get your own appleID now.  It's free.  Don't share, you will run into many issues going forward.  appleID's are meant to be shared by more than one device, but with all being used by the same primary user.  That is... use the same one on YOUR iPhone and iPad or HIS iPhone and iPad, but don't mix devices for 2 people.  Go here to create an appleID. 

You can still use "family Sharing" to share iTunes purchases.