can I change the last name of my son to mine, and also obtain full custody..
You can if the Court orders it. First you have to petition the court, and prove your allegations that would justify this - which would be unusual. It is not a do-it-yourself process, and it is quite complex. Look through this site, and others, to locate a family lawyer in your area to explore what options are available under your specific fact situation. Good luck.
It appears that you are in Harris County based on your zip code. I'd call Patricia Bushman at 713-807-9405. I rent space in her office. Her first appointment is free & she takes payment plans.
You can also look on this website or on www.avvo.com.
Merry Christmas!