How could I possibly know if I can use the name 'LexCorp' for a real company. LexCorp is the company of Lex Luthor in the comic books of DC.
You can check the USPTO trademark database, to see if it is a registered trademark. You could also ask LexCorp about their claim that it is a registered trademark of DC comics or WB, though their CEO appears to be a criminal mastermind and might not tell the truth. There is some unclarity as to the latter point (criminality). USPTO includes a "don't rely on the database" disclaimer, so maybe it is registered and it just doesn't show up