B.J. grew up around there, and went to work for his cousin Wilma at some point.
B.J. wanted to take Anya Oliwa to Mesquite to see the dawn light.
It can also refer to a type of desert plant (often used to flavor BBQ sauce) (but it is capitalized in the game text).
Behind the scenesEdit
This is likely a nod to the original location where ID software was founded. Mesquite, Texas, U.S.A (February 1, 1991).
In the original games, and up to Wolfenstein (2009) B.J. had a western to mid-western accent and its implied that he was from Milwaukee.