Hiring: Can You Legally Use a Pseudonyms on Your Résumé

My question involves labor and employment law for the state of Texas. I have three questions specific to resumes and not applications:

1. Is it legal in the USA to use a pseudonym instead of a real name on a resume?

2. Can listing earned/legitimate degrees under the birth name associated with a pseudonym on a resume be considered resume fraud?

3. Can prospective employers conduct a background check from resumes without consent?

Thanks.

Hiring: Can You Legally Use a Pseudonyms on Your Résumé