sounds like someone is trying to prove some type of discrimination based of off name (gender or racial stereotyping).
That said, i do know employers who will do a cursory 'net search on names and locations prior to ever setting up an interview. I haven't seen them do a full background check, but realize FCRA only applies to third party background checks not internal ones.
If you use a 'pseudonym' you better do your own investigation into the name first! And honestly going into a new hire process as James Jones and telling HR your real name is Kevin Smith is going to put a ? on your employment file pretty immediately. Now I've had plenty of people who use nicknames for first names.
You also need to be careful about what you are attesting to in any application you sign. Some do say that it covers not only the application but any resume/cover letter/documentation that you have provided. And I would say a "pseudonym" means you are hiding something and not telling the truth.
In most "at will" states an employer could pull the job first day for you having done so. Especially if you also do so on a background check form.

