As an engineer I am required to do site visitations, and I fly within the US main land all the time. I have never had any issues boarding nor getting off a plane. You will be fine, just make sure that the name on your flight ticket matches letter by letter to the name shown on your TX DL.

Meaning that if you have a gazillion names and last names like I do (I'm hispanic and we're rich with the names), then all of those names and last names shown on your DL must also match the names on your flight ticket.