If your ticket is already printed out, you may give it to the person that will use it for admission and they will be able to get into the event with no problem.
However, if your guest is going to pick up the ticket at will call, they will be asked to show an ID that matches the name on the ticket, so the will call name will need to be updated.
You can update the will-call information yourself here by following the instructions here: How do I change the will call name on tickets?