I'm trying to suggest a research strategy to recommend to you. One stumbling block for me is the implication that the birth parents were married---your knowledge of the birth father's name implies just that---versus the use of a maternity home, which is usually for unwed women pregnant for the first time.
If you wish to learn the names of your maternal and paternal grandparents, consider searching the Texas portion of the federal census of 1930, which Ancestry.com has indexed and placed online for the benefit of its subscribers. Ancestry has message boards for various counties in the USA, and that is where you can befriend genealogists with experience in looking up the census.
If you wish to apply for full copy birth certificates of your birth parents, or their marriage license or death certificates, you can find addresses and fees in the online publication entitled, "Where to Write for Vital Records" (41 pages) :
http://www.pueblo.gsa.gov/cic_text/misc/vital-records/vital....The online Social Security Death Index, which is mostly for post-1962 deaths, is at :
http://worldconnect.rootsweb.com/cgi-bin/igm.cgiThe Rootsweb version of the SSDI allows you to post an annotation to the decedent's entry by clicking on "Add Post-em" and explains how to apply for the SS-5 form.
I have posted dozens of comments of an educational nature on the "Adoption Queries" board at Ancestry.com.
Reg Niles
RegNMINiles@cs.com