Josh Tillman had recorded eight albums under the name J. Tillman when he had an epiphany, prompted by his first (but not last) experience with a hallucinogenic drug: He should change his name as a way of rebooting his career. He was unsatisfied with the somber, sedentary folk songs he’d been making — “sad bastard music,” he called it — and wanted to spring free his sense of humor, absurdity and playfulness.

Mr. Tillman, who had also played drums in the indie-rock band Fleet Foxes for four years, was readying the release of his 2012 album “Fear Fun.” A friend asked about the moniker, and Mr. Tillman unveiled it: Father John Misty.

“He was like, ‘No! Do not call it that,’” Mr. Tillman said with a chortle. He was sitting in a hectic hotel lobby in downtown Manhattan, two days after a “Saturday Night Live” debut that exposed him to new admirers, skeptics and online hecklers. “And I said to him, ‘Yes!’ Because that’s my [gosh-darn] personality. I have a weird, cheap petulance. People hear it, and it fills them with loathing: ‘What kind of [chump] calls himself Father John Misty?’ But when I hear it, it makes me laugh. It never gets old.”

After adopting a ridiculous pseudonym, Mr. Tillman emerged, belatedly, as a sterling songwriter. He has a side gig, writing pop songs with Lady Gaga and Beyoncé, which might surprise fans of Father John Misty’s ruminative, smutty, increasingly-soft rock. Two years ago, he released “I Love You, Honeybear,” a record about the male psyche, and all the insecurity and fear it generates when faced with the prospect of monogamy. It was widely picked as one of the best albums of 2015.