King claimed she would refuse to play on the MCA if she was still competing today, and encouraged others to "look inside their heart" to consider doing the same.
"I guess you got to take it just as how she was as a tennis player", Kyrgios said. "It's a public facility".
King said a series of comments made by Court about the LGBTI community were simply unacceptable.
"I was fine until lately when she said so many derogatory things about my community".
King's remarks appeared to catch tournament officials off guard.
Speaking to i ahead of the Australian Open, Dale Park, the co-convenor of the Victorian Gay and Lesbian Rights Lobby, said of renaming the Margaret Court Arena: "Mrs Court's sporting achievements are unquestionable, but her consistent attacks on the LGBTIQ community, including a fellow Australian tennis player [Casey Dellacqua] and their family, fall well short of community expectation".
She said she wished Court was at the Australian Open this year so they could have an open discussion about the issue.
Craig Tiley, Australian Open tournament director and CEO of Tennis Australia, said there were no plans to change the name of the stadium and that Court's views did not echo those of the organisation or the sport.
"Mrs Court's ongoing claims that tennis has been infiltrated by lesbians and that older female players have corrupted younger female players are homophobic at the very least and paint same-sex attracted people as predatory opportunists".
"I completely agree with the freedom of speech.But when you start comparing good people to some of the most evil people in history due to their sexuality I'd say it comes pretty damn close to preaching hatred".
'Maybe it's our community, the LGBTIQ community (why) people might feel differently. But we're all God's children.
"I probably don't think it's appropriate to have her name [on the stadium]".
"I respect what Billie Jean said", Stephens told reporters. So, that's all the devil - that's what Hitler did and that's what communism did: got the mind of the children. In another interview she said transgender children were "the devil".
The stadium was renamed after Court in 2003. King expressed disappointment at her absence, said she had been looking forward to seeing her.
The 74-year-old's advocacy extended to naming the showcourt after her friend Margaret Court, but King said she could no longer support the honour.
The former WA Liberal Party president said there should be "no thought of changing the name" of the arena. They are not the views of our organization and not the views of our sport. "We're inclusive, diverse and equal", he said.
Margaret Court Arena generally hosts five marquee matches per day through the first week of the tournament, and is sold as a separate ticket from the rest of the grounds.
"It is now clear exactly who Court is: an unbelievable tennis player, and ... a homophobe".
- Open letter re Qantas: 'As you will know, I have represented Australia many times and have the proud record of never losing a tennis match while playing for my country.