Your search would be a lot easier if the adoptee was born in New York City, which publishes annual lists of babies born there, and some with their adoptive names a year or two later. His birthplace and date of birth are not in your query. You say you have his original birth certificate.
If anyone reading this board wants further details on the annual lists, go to:http://boards.ancestry.com/topics.adoption.adoption/19249.1/...
If the adoptee’s adoptive surname is learned, enter the full name and the date of birth on the website known as Veromi.net. If the surname is unknown, try the first name and the d.o.b. without the surname. If Veromi has more than 100 hits, limit the search to Texas or whatever state you wish.