I'm not sure the question was so much about using a pseudonym in business, but whether it is legal to use one on official incorporation paperwork, which requires the full names and addresses of all corporate officers. And it doesn't seem like it would make sense for it to be legal to give a false name on this paperwork. These are the rules for incorporation in Arizona:
http://www.azleg.state.az.us/ars/10/03202.htm
Dunno, seems like for official government paperwork, they'd need to know all of the corporate officers' real names and addresses...know who to hold accountable if there were any issues.