Check your settings. You've probably got your e-mail address set up as your caller ID. To check:
Go to your Settings app and scroll down to Messages. Find the line "Receive At" and select it. At the bottom of the next tab, press the line titled "Caller ID." Ensure the check mark is on the line you want as a caller ID (I use my e-mail address so I can see the same message on my iPad - YMMV).
Hope that helps.
Marilyn