I hope I'm on the right general area here.
How do you make it so that txt msgs are private from anyone even if they're on your plan?
Feeling a little violated..
If you're referring to what's available via My Verizon, the Account Owner has access to all text logs for all phone lines, but not the message content. However, if you're using Verizon Messages and someone knows your line's My Verizon log-in credentials, then they can see the text content.
Are you asking how to prevent others from seeing the content on your phone? A little more info is needed to help answer your question.