If you have been using your Apple ID email as the contact up until this point, it should not matter at all, that your phone number is not being listed.
Turn Messages Off. Settings>Messages>Off. Restart your iPad and then turn Messages on again.
Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.
If that does not work, when you post back, explain what happens when you try to send a Message - any details at all that you can provide would be helpful.
Using FaceTime http://support.apple.com/kb/ht4319
Troubleshooting FaceTime http://support.apple.com/kb/TS3367
The Complete Guide to FaceTime + iMessage: Setup, Use, and Troubleshooting
Troubleshooting FaceTime and iMessage activation
iOS: FaceTime is 'Unable to verify email because it is in use'
Using FaceTime and iMessage behind a firewall
iOS: About Messages
Set up iMessage
iOS 6 and OS X Mountain Lion: Link your phone number and Apple ID for use with FaceTime and iMessage
How to Set Up & Use iMessage on iPhone, iPad, & iPod touch with iOS
Troubleshooting iMessage Issues: Some Useful Tips You Should Try
Setting Up Multiple iOS Devices for iMessage and Facetime
FaceTime and iMessage not accepting Apple ID password
FaceTime, Game Center, Messages: Troubleshooting sign in issues
Unable to use FaceTime and iMessage with my apple ID
How to Block Someone on FaceTime
My Facetime Doesn't Ring
Send an iMessage as a Text Message Instead with a Quick Tap & Hold
To send messages to non-Apple devices, check out the TextFree app https://itunes.apple.com/us/app/text-free-textfree-sms-real/id399355755?mt=8
How to Send SMS from iPad
You can check the status of the FaceTime/iMessage servers at this link.