Is the Joker’s real name Arthur Fleck also in the comics? Should we consider Joker (2019) as establishing this name? Like in every movie, Catwoman is Selina Kyle, Penguin is Oswald Cobblepot, and Harley Quinn is Harleen Quinzel.
No, the Joker has never been called Arthur Fleck in the comics. Some versions of the character are known to have the real name Jack Napier – it was first used for Jack Nicholson’s big-screen Joker and later in Batman: The Animated Series and the White Knight story arc, amongst other places. In some flashbacks scenes to his pre-Joker life he had the first name Joe, though he could be lying or misremembering in these cases. In most versions of the story, his birth name is completely unknown, perhaps even to the Joker himself.
Realistically I’d say that the Joker film is meant as a stand-alone piece, a “what if” story that’s not meant to affect comic canon in any meaningful way. However, if we wanted to tie in Arthur Fleck with the broader mythology of the character, we could say that he’s one of the Three Jokers that are currently active, as Batman learned from the all-knowing möbius chair. Perhaps Jack Napier is the “gangster” version of the Joker, “Joe” is the sadistic, Batman-obsessed Joker of The Killing Joke, and Arthur Fleck makes up the trio. I don’t think that’s how it will play out, but it’s one way to make the film fit in with the stories we know.