Who’s left? By “public figure” I mean anybody whose name might have been commonly known at the time. Could be an actor, a writer, a musician, a politician, a sports figure… anybody.
The only person that jumps to mind for me is Elizabeth of York.
Forces sweetheart Vera Lynn? Very popular during the war.
Start with Simeon II of Bulgaria, a.k.a. Simeon Saxe-Coburg-Gotha, Tsar of Bulgaria during part of WWII and in 2001 elected Prime Minister of Bulgaria.
And then there’s Norodom Sihanouk, King of Cambodia during WWII who is also still alive. Although he has abdicated in favor of his son, he still has some honorary rights.
Otto von Habsburg never took the Austria-Hungary crown, but was a prominent figure before, during and after WWII. He has served in the European Parliament among other positions.
And that’s just some of the royalty.
Stan Musial was already a star ballplayer during the war. While not at all well, he’s still with us.
While Mickey Rooney and Shirley Temple were both past their prime by the time WW2 broke out, they were still very much household names at the time, and they’re both still alive today.
Deanna Durbin – a big singing and movie star of the 40s – is still alive.
Edited thread title to indicate subject.
Colibri
General Questions Moderator
Dolores Hope, though not as famous as her late husband, Bob Hope, is still alive.
Olivia DeHavilland and sister Joan Fontaine…both still alive and not talking to each other.
Hockey players Elmer Lach and Milt Schmidt (the latter was a member of Boston’s Kraut line in those glorious PC days. Later they changed the name to Kitchener to reflect where Schmidt, Dumart and Bauer were from, Kitchener itslef being a name change).
The Queen of England. Or Britain, or Great Britain, or the British Empire, or whatever you nitpicky types want to call it.
That must be who the OP means by Elizabeth of York, although I’ve never heard her referred to by that name.
Interesting question though - most of the people I thought of turn out to have died within the last few years.
Nanette Fabray was making films and acting on Broadway throughout WWII.
I thought maybe Dick York’s sister. 
June Foray was voicing cartoon characters as early as 1941, including Oswald the Lucky Rabbit in 1943, though most of her early work was uncredited.
T. Boone Pickens
George H. W. Bush
Celeste Holm was acting on Broadway during WWII.
If it’s expanded to ‘anyone famous now who was born before WWII,’ it’s going to be a very long list indeed.
Maybe I got it wrong, but I believe that’s her handle sans the changing royal title. What would you call her, Elizabeth Windsor?
Maureen O’Hara made movies throughout WWII, including Oscar Best Picture, How Green Was My Valley in 1941.
SNL announcer Don Pardo was a war reporter for NBC radio during WWII.