If “Mean Streets,” “Taxi Driver,” “Raging Bull” and “Goodfellas” had never existed, Martin Scorsese would still occupy an exalted place in American cinema, strictly for his documentaries. His films on The Band, George Harrison, Bob Dylan, New York City, Italian opera and Fran Lebowitz constitute a singular catalog of movies, all of which are purely entertaining while exploring the complicated space where public image, art and personal history co-exist. Mr. Scorsese’s evident interests as a nonfiction filmmaker come together in “Personality Crisis: One Night Only,” his study of a less-than-obvious subject— David Johansen , onetime New York Doll and proto-punk rocker, who for several decades has also performed as Buster Poindexter , pompadoured lounge lizard and crooner of standards, novelty songs and the work of David Johansen. This is how Mr. Scorsese, credited as co-director with David Tedeschi , frames this portrait of a New York institution: during an early 2020 gig at the upscale Café Carlyle (which Mr. Poindexter refers to as a “boîte” and a “joint”), where the alter ego performs the work of the original.

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