PARIS — Show Court 1, one of the biggest stadiums at the Australian Open, was rechristened Margaret Court Arena in 2003 to honor the player who dominated women’s tennis in the 1960s and still holds the record for the most Grand Slam titles.

It is unclear what the stadium will be called when the tournament begins in Melbourne next January.

Court, 74, now a pastor in Perth, has reignited debate about her legacy and how the sport should celebrate her by making a series of inflammatory comments recently about gays and same-sex marriage. Her beliefs are not new — her public comments first stirred protests in 2012 — but her unflinching remarks have provoked some current players to say they would object to playing on a court named after her.

“I think it would be a good thing to see if the Australian Open can maybe change the name of the stadium,” Richel Hogenkamp, who is gay, said after winning her first-round match Monday at the French Open, where talk about Court has commanded unusual attention. “Because I think if you’re in that kind of position, maybe some players, they don’t feel so comfortable playing in a stadium named after Margaret Court.”