I had something similar happen to me twice.
One i cought the problem early enough, called the agent and he had it changed without any issue - since it was an error and not a different person. The agent also told me it was his responsibility because he made the mistake. So clearly i would insist that the agent correchts his mistake. I would also threaten him that - in case somebody catches it and you are not allowed to fly and have to buy a last minute ticket - you would hold him liable for any additional costs.

Second time i did not catch the error until after i boarded. Nobody noticed a missing letter in my first name before. The risk is that the airline sees it when you check in or the passport check at security find it. Unlikely with such a small mistake, but possible. Not sure what happens then.

Why should US immigration be a problem? Are they looking at your ticket?