Upvote:6
Yes, the booking is still valid since the ticket is issued to the person.
Keep in mind, this is very rarely a problem since even if the one spouse takes the other's name, that process takes a long time to fully complete.
In the interim, the spouse will still have valid ID in their old name to use for many, many scenarios. It's not just air travel that's affected. A typical case would be the Honeymoon trip where the tickets would likely be booked under original names with both parties able to still present valid ID in those names, including Passports.
One piece of advice you will often see is that the spouse changing names should also carry a copy of the Marriage License or other document attesting to the name change.
If a trip is booked many months in advance, then that has to be evaluated individually depending on whether or not it's international and if you expect to have the Passport reissued. Here, the most important thing is for the name to match, old or new.
If you are certain to have new proper ID, then the ticket should be booked in the new name.
Many, but not all, airlines will do one no-fee name change in the case of a legal name change.