Hello Masans,
If the person you are messaging with also has an iOS device or a Mac running OS X Lion or later, then the sender can send a message using an Apple ID.
There is a Messages setting that will allow you to select whether you want new messages to be sent from your phone number or Apple ID, and your friend that is messaging you may have that set up.
You can go to Settings > Messages > Send & Receive > Start new conversations from: to see whether you ar sending new iMessages from your phone number or from your Apple ID. You can find more information in the full article here:
iOS: Using Messages
http://support.apple.com/kb/ht3529
Also, if you would like a name to be at the top of the message instead of an email address, you can add the email address to that person's contact information.
Thank you for using Apple Support Communities.
Best,
Sheila M.