It won't correct it for previously booked tickets, only new ones. Your best bet is to call and ask them to correct it. In my experience there are no practical consequences to it being wrong except that they'll usually lose TSA PreCheck if they were otherwise eligible, but legally it's supposed to be correct. (Having said that, it's been a while since I tried--I suppose it may cause more issues at airports where your ID is checked against the airline data in lieu of the TSA scanning a boarding pass.)

(I seem to recall that it used to be possible to correct it on united.com by pulling up the itinerary, but as best I can tell that functionality is gone now.)