If paternity has been established, then there are steps you must take with him regardless of how involved he is or whether he has paid support.
If he is willing to consent to the name change then you just have him sign the waiver and go. If he won't you'll have to serve him.
In either case you have to convince the judge that the name change is in the best interest of the child.
Note the name change doesn't change the fact he is still the father nor does it free him from any court-ordered support obligations.
These following links are from Collin County, but they're indicative of what you need to do anywhere in the state.
http://www.collincountytx.gov/law_li...othParents.pdf
http://www.collincountytx.gov/law_li...rOneParent.pdf

