I’m curious if any writers using pen names, thespians using stage names, or criminals using aliases managed to keep their true identities secret until their deaths (and beyond?).
Jack the Ripper comes to mind immediately. Who else?
The cross gender jazz singer who kept her secret until death. Billy something or other.
That is Billy Tipton.
The Black Dahlia killer?
I’m not sure that Jack the Ripper would really fit into this category, because he was never caught by the police. It’s not like someone was going around calling himself “Jack the Ripper” and refusing to tell people his real name.
In answer to the OP, I recall at least one or two stories (but can’t provide details or a cite) of women disguising themselves as men to serve in the Civil War and not being found out until they were killed in battle.
The Jack the Ripper name came from some letters that were written by someone claiming to be the killer. If it really was the killer who wrote those (opinion is divided on that, although most sources lean toward saying they were only hoaxes) then he would definitely qualify for the OP.
Along the same lines, I think the Zodiac Killer chose his own alias and nobody figured out who that was. The Black Dahlia killer wouldn’t count though, as that’s just the victim’s nickname with “killer” added to the end and the murderer didn’t do that.
My great-grandmother wrote two books as Edesse Peery Smith. We all thought Edesse was her actual name; everyone called her Eda. (The middle name, Peery, is misspelled on that Amazon page; it’s my middle name as well.) Not until she died, in 1981, and my father and uncle were going through her papers and such did they find out her real name was Olga.
My father later recalled having had a conversation with her in the 1950s when she, apparently apropos of nothing, asked him if he didn’t think “Olga” was a terribly ugly name.
I don’t believe anyone knew that the “von” in “Erich von Stroheim” was fake until after his death.
Even from childhood, my grandmother and great-aunt were called slightly different names than their baptismal ones. Gramma was Lennie Lucile, always called Ludy or Lucile, and my dad (her son!) believed until her death that her given names were Ludy Lucile. Similarly, Mary Lillian was always called Mary Jane, and once again, we only found out after she passed.
We’re still not sure as to whom B. Traven was as birth- even the identification of him as Ret Marut is a pseudonym
The gender of the Chevalier d’Eon was a mistery until his death.
Actors E.G. Marshall and Stubby Kaye. Their real names were mysteries until after they died.
Dan Cooper. Assuming that a) that really wasn’t his name, and b) he’s dead. (Probably safe assumptions)
Quorthon did a pretty good job.
Cecil Adams almost fits into this category, though by this point, just about everyone assumes he’s Ed.
Darn you, Peter Morris! You stole my answer! 
Seriously, Chung Ling Soo sort of fits this category because the general public just took it at face value that he was Chinese. Of course it didn’t help matters any that he always gave press interviews dressed in full Chinese regalia and had an “interpreter” to translate for him. Those in the magic community knew he was William Robinson and that it was all an act.
My grandfather changed his name when he came to America. Nothing unusual about that, except that he and my grandfather were always a little cagey about what his original name actually was. We think we know, but we aren’t 100% sure, particularly of the spelling of the original name.
Billy had a brother named Bill. I worked with Bill for a number of years while “Billy” was alive. We knew that Billy was Bill’s brother (they actually looked quite alike) and thought it was rather odd that Billy had pretty much the same name as Bill. When anyone brought up the subject with Bill he would get angry and make some comment about “Billy” being a stage name and that he pretty much had nothing to with his “brother”. Bill retired before Billy died so he never had to deal with any explanations at work. I saw him a few years later at a company golf outing and figured it was for the best that I not bring up the subject. So I never figured out whether Bill was ashamed of his sister or whether his anger was staged in order to help maintain her secret.