It's not using RyanAir, rather using Orbitz's multi-city search. So basically it's just an extra flight tacked onto what would normally be a roundtrip itinerary. There's no mention of birthday or passport number to my knowledge, but I don't think I'm running any other risk than missing the flight and cancelling the rest of the itinerary.
Originally Posted by WillTravel
Did you enter your birthdate or passport number at any point?
I think in theory the airline can ask for the credit card used to make the booking, but check the Ryanair site.
Other than that, how will Ryanair, or even yourself for that matter, know if the ticket was booked for you or your dad? Maybe when you booked the ticket, you meant to book it for your dad after all - how could you have done it any differently?