I think you have this problem, because you are using the same email on two or more devices. Anyway I will provide you with two methods, because i had a similar problem like yours back in the day.
- Method 1: (not an universal fix)
Go to Settings > Notifications > Messages, turn off notification center
Then Go to Settings > Messages, turn off iMessage
Reboot the phone
Turn iMessage notifications back on, then turn iMessage back on, in that order.
- Method 2: (if you are using the same iCloud account on two or more devices)
Go to: iMessages > Settings > Send & Receive > turn on all your phone numbers and email.
Most importantly, set "Start new conversations from" your phone number, not from your email addresses.
EDIT: If you update to the latest iOS version this problem will be fixed by itself.