My question involves marriage law for the State of: Texas

I'm a newlywed and trying to figure out the process regarding changing your middle name as well as your last? Has anyone done this before? i want to take my husbands last name but also get rid of my middle name entirely and take on my grandmothers maiden name as my middle. Can I just change this when I go to the DMV to change my last name? Just tell them my new middle name, is it that easy?

Thanks.