I work in the travel industry so I see similar things everyday.
Generally airlines only require your first name and last name that are on your passport. The exception being USA who require full passport details.
Can’t really comment of the $450 to change it. It depends on the individual rule of the airfare. The cheaper it was to buy the more restrictive the airfare rules. So if your fare dosn’t allow changes (which can be quite common) and you wanted to get your middle name on the ticket chances are you will have to purchase a new ticket.
I would call the airline directly and check if they require your middle name on the ticket.