“Can I use my [mother’s/brother’s/friend’s] address on my Driver License?”
I get asked variations on this question all the time. The rule in Texas is you must use the address where you reside (in other words, where you put your head at night).
If you move, you have 30 days to contact DPS and request a new Drivers License. This also applies to ID cards.
For info on how to change your address, see the DPS page on changing information on your license.