If you booked the flights via the call centre and it was done recently, ask them to review the call. If you gave them the correct spelling and they haven't applied it correctly, I'd expect Virgin to make good on their error without any cost to yourself. They will only hold the recordings for a limited time, so if you think they have made the error, I would contact them to escalate without delay.

I definitely would not advise trying to fix this at the airport, as you may find there is no potential remedy, or an extremely costly one.