Are you using iMessage or standard SMS? is the icon Blue or Green?
Firstly, in the Messages app, your outgoing message bubbles are either blue or green. That color coding is key to knowing what's what. Let's start with blue ones: If they're blue, that means it is an iMessage going from one Apple device
Try contacting Verizon CS. Others that ported their numbers over and experienced this issue were able to get it resolved by calling CS. I cant recall what the issue was but it was something they were able to fix on their end.