If it's very important for her to fly then I would advice you:
back her up same day with a refundable ticket with her old name just in case she will be refused to board.

Check in online the night before, print out the boarding pass and take with you the appropriate papers just in case they saw the wrong name, and don't talk about that with the check in agent, the most chances that they wouldn't see the problem (even they slip the passport in the reader).

if she have a FF with her new name then she should go with that card along with printed boarding pass to the check in, the agent will search for her name in the system and then ask for the passport just to check if it's valid etc, as this is the regular way of that process, stay calm you have big chances to go through.

if you can avoid checked luggage.

remember if you are lucky in the states you have to repeat again in the EU and none can assure you succeed so you will have to back up again with OW refundable ticket.