As far as I know, airlines do not change names on tickets, regardless of whether a FF account is updated to reflect the name change.

A person whose name changes after a ticket is issued is accommodated, but needs to be prepared to endure some hassles, which may include having to produce various documents, being yelled at for offering certain documents, secondary inspection, and the like. Each encounter likely will vary. These can all be overcome with patience and allowing extra time for the check-in process.

What does not vary is an airline's refusal to change the name on a ticket.