Welcome to FlyerTalk!
I do not know the answers to your question about name changes for airline tickets.
I do know that one can get a passport issued on an expedited basis if your travel is less than 2 weeks away. A few months ago, I had such a situation, went in to the passport office in the morning and picked up the new one in the afternoon.
I would guess that if you have proper documentation - new passport with new name, old passport for his nation of origin with original name - the airline could change the ticket name. And yes, US citizens are supposed to enter and leave the US on their US passports.
With all the stories of delay and mistreatment of foreign nationals at US ports of entry, I think I would not delay or reschedule the citizenship oath. Re-entering as a US citizen is probably easier.
Good luck!