Texting and phone I am texting is asking for my name
It sounds like you are just trying to send a regular text. 

Here's how to do it:
Open the Messages app, (tap "Messages" in the upper left corner if you are in a thread), tap the compose icon, enter the recipients phone number (I've never had it ask for my name), then type your text.

If you are using the Messages app, it should not ask you for your name.