That's one of the questions Australia's highest court is considering, after hearing arguments in a long-running trademark dispute between the pop star and a fashion designer with almost the same name.
Issues of reputation and timing are at the heart of the stoush, with lawyers for both sides arguing the other's trademark should be ruled invalid.
Designer Katie Perry, who now goes by Katie Taylor, has been locked in litigation with the Firework, Dark Horse and Roar singer since 2019, but the saga goes back much further.
Ms Taylor registered a trade mark in 2007, and says she didn't know of Perry's existence at the time.
But it was a different story when she re-registered a year later, with documents lodged in the High Court showing she'd heard I Kissed a Girl on the radio and bought it on iTunes.
More than a decade on, Ms Taylor took the singer to court, accusing her of infringing the "Katie Perry" trademark by selling branded shoes, clothing and headwear while on tour in Australia.
Initially the Federal Court upheld the Australian designer's claim, but the court's full bench later overturned the ruling.
In the High Court on Tuesday, references to Rhianna, Taylor Swift and Lily Allen bounced around the room as five judges heard Ms Taylor's appeal, grappling with the question of who should have the rights to the Katy/Katie Perry name.
The designer sat in the front row of the courtroom's public gallery wearing a black jacket and pants, accompanied by her mother and stepfather.
Her lawyers argued shoppers were savvy enough to distinguish between the two spellings, and would not think Ms Taylor's clothes were linked to the pop star.
They also told the court there was no way of knowing how famous Perry would become when the trademark was first lodged.
"Rapid fame can be fleeting, it can be ephemeral," Ms Taylor's lawyer Christian Dimitriadis SC told the court.
But Perry's legal team hit back, saying Ms Taylor shouldn't have waited more than 10 years to complain about her trade mark being infringed.
"She could've written a letter, she could've written an email... she simply had to do something to object and she did nothing in all that time," Matthew Darke SC said.
He also described the difference in spelling between the two women's names as "minor," suggesting consumers may have thought they were buying Perry's merchandise when they were in fact buying Ms Taylor's.
The High Court will hand down its judgment at a later date.
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