You should be fine as long as you bring proof of identity. It is not a big risk.
If you miss your ceremony you will have to try to get it rescheduled. If you're going to be gone a long time I'm not sure how easy that is.
My answering this question does not form an attorney-client relationship. Always retain a qualified attorney before taking any action.
You have to listen to the Immigration Officer. Your new Certificate of Naturalization, with a second sheet attached to it, which shows your name change is a legal document, and with your passport, carry the same legal proof that this is the same person. So there is nothing to worry about, as long as you have the original Certificate of Naturalization with you when you travel.
Contact attorney Gintare Grigaite, Esq. at 201-471-7989, located in New York and New Jersey. Answers on AVVO do not constitute legal advice and do not form attorney-client relationship. Always consult an attorney for a legal advice.
Go to your oath ceremony, travel with both passports. Not sure where you are from, but having a U.S. passport is a good thing. Missing an oath ceremony or rescheduling is not. Until you are sworn in under oath you are not a U.S. citizen.
You can get a U.S. passport quite quickly, and most countries have consulates in New York City.
Nevertheless, I would suggest traveling with both passports, you can have dual citizenship (usually, depending on the other country's rules) and you can travel under your foreign passport alone if you wish.