The "current name" is exactly that: whatever the person's current name is. The citizenship application form also asks for previous names used, and evidence of all name changes must be provided (e.g. marriage certificate, name change certificate, divorce record).
In my partner's case, when we apply in the first half of 2024, she will enter her married name (as that is the name she is currently using) on the application form, fill in her maiden name in the section of the form asking for any previous name used, and provide our foreign marriage certificate as supporting evidence.