How old is your GF? You mention HS ID so is she less than 18? Children are not required to present ID.

Just say she is under 18 and if the TDC gives you an issues then just pull out the HS ID.

If she is over 18 then present her gov't issued ID.

I thought due to the whole RealID fiasco it became against policy to issue drivers licenses with any thing but the full legal name. Most states didn't implement RealID, but still adpoted many of the policies. Why would you think that a newly minted DL would have anything less than the full legal name?