Two… Sort of.
The former star of Wall Street and Fatal Instinct that you know as Michael Douglas (or perhaps Michael Zeta Jones) never played Batman in a movie.
The actor you know of as Michael Keaton did play Batman in the two Tim Burton Batman movies in the 1980s. It turns out that Michael Keaton’s name is actually Michael John Douglas.
In a 2017 appearance on The Late Show with Stephen Colbert Michael Keaton explained that he wanted to use his real name, but there were already two Michael Douglases in the union – Mike Douglas the talk show host, and Michael Douglas the star of The Streets of San Francisco and Hank Pym from Ant Man.
He uses Michael Douglas in his private life but has to use Michael Keaton as his stage name. He chose Keaton on a whim and it is a name of no particular significance.