This man is the husband of Missy Cooper, the father of her son and the brother-in-law of Sheldon Cooper.

Sheldon went to Texas to aid in the birth of his first nephew because Missy's husband had been in a terrible motorcycle accident and was recovering from it. Neither Sheldon's nephew's name nor his brother-in-law's name are mentioned. 

In "The Bow Tie Asymmetry", Missy tells Raj that she and husband are separated even her her mother seems to wants to ignore that fact and that she is also pregnant.