EI does not hold maiden name so you were 100% right to terminate the call. The calls are all recorded so they will ask what time and from what number you called from to pull the recording.

Booking reference, email and phone number, possibly the last 4 digits of the credit card used (not all bookings have a credit card tail visible). Is what they need. Phone number is irrelevant if the caller ID matches

The lovely team in Jericho in NY are the only way to go, should be online by now