One apple ID for multiple family members

We are new to the Iphone products.  We have shared an Apple ID since christmas with my two children to help control what they are downloading etc on thier Iphones.  Currently for some unknown reason when one of my children send me text message it comes accross to my phone as an email address which is what is used as our apple ID from when I originally got us set up for the ipods from years ago.  since getting the Iphones this all of a sudden seams to be an issue with only one of our phones. 
Any suggestions how to fix this?  We deleted the icloud accounts, and have done the "soft" reimage per verizon wireless.  Do we really have to set our children up with thier own email addresses and Apple ID's too? 
Any suggestions would be helpful.
thank you,

To fix this go to Settings>Messages>Send & Receive and do one of the following:
1.    Either uncheck the email address shown under "You can be reached by iMessage at" on both phones; or
2.    If you want to continue to receive iMessages at this email address on one of your phones, on the other phone tap the Apple ID at the top, sign out, then sign back in using a different Apple ID (so both phones will be using a different Apple ID for iMessage).  Note: you can continue to share an Apple ID for purchasing from the iTunes and App stores.  It does not need to be the same as the ID you are using for iMessage, FaceTime and other services.
Because you are  using the same Apple ID for iMessage. To prevent this, on one of the phones go to Settings>Messages>Send & Receive, tap the Apple ID, sign out, then sign in with a different Apple ID.  Note: you can continue to share an Apple ID for purchasing; it does not need to be the same as the ID you use for iMessage, FaceTime, iCloud and other services.
Also, to prevent merging your calendars and contacts if you are syncing these to the same iCloud account, be sure to set up separate iCloud accounts on each phone with separated IDs.