I actually like that one, too.
Zimmerman was being used.
Schweitzer was associated with a lost friend. And, it and Van Gogh kind of belonged to existing historical figures.
Joe just showed up too late.
Kenneth is the silver medalist, a fine sobriquet that (like the surviving holo-family) were casualties of the Reset Button). No reason not to use it.
But Schmullus was given by a person the Doctor loved, in honor of someone who shared traits she admired. And a person who risked her life to help Voyager later on. It would have been eminently, hearwarmingly logical for the Doc to stick with it.
Just as "Night" was the perfect episode to quietly correct the utterly stupid mistake of Harry's rank, "Lifesigns" was the perfect episode to resolve the issue of the Doctor's name. Both opportunities were missed, par for the course for Voyager.