This isn't being cused by iCloud. It happens when you both use the same Apple ID for iMessage. To fix this you have two choices:
- On one of the phones go to Settings>Messages>Send & Receive, tap the ID, sign out, then sign back in with a different ID. Note: you can still share the same ID for purchasing in Settings>iTunes & App Stores; or
- On both phones go to Settings>Messages>Send & Receive and uncheck the email address(es) shown under "You can be reached by iMessage at".
Also be sure you aren't using the same ID for FaceTime or you'll get each other's FaceTime calls. If you are, one one of the phones go to Setings>Facetime, tap the ID, sign out, then sign back in with a different ID.