According to sources, Jeff Gannon's real name is not, in fact, Jeff Gannon. According to the same sources, his White House press credentials list him as "Jeff Gannon" - they let him use his pseudonym -- even though married female reporters, who use their maiden name professionally, are given credentials with their married name and aren't allowed to be credentialed under their maiden names...
...not sure why this isn't clear, but the point is that he's allowed to be credentialed under his professional pseudonym even though women whose "professional pseudonyms" are their maiden names aren't.