The customer service representatives have no option other than to say the name on the ticket must match the name on the passport exactly. Your mileage may very, but name suffix is endlessly an issue. The suffix is on the passport but has never been associated with ticketing on any airline. The issue is with immigration, not the airline. In the event immigration is looking for a reason to refuse entry the mismatched name is low handing fruit and the airline is responsible for the flight home. If you haven't traveled extensively the better option is first and last name only without a prefix or suffix or middle name as the booking systems don't handle names very well. In my opinion, once you have circled the earth 10 times the airlines and immigration know who you are before you get there and the name on the ticket is secondary.