I set up my iphone and now my email appears as name on my text messages?

see if this support article helps

Add or remove your phone number in Messages or FaceTime - Apple Support

I believe your issue is that you need to go to Settings > Messages > Send & Receive and select the phone number under the section 'Start New Conversations From'

Note that when you do this, you can't just continue with the existing message thread. You'll need to create new message threads rather than replying within an existing one.