'I was fine until lately, she says so many derogatory things about my community.'
In an interview with Vision Christian Radio last year, Court said transgender tendencies were 'all the devil'.
'What confusion to a child. I get confused talking about it. You can think, 'I'm a boy', and it affects your emotions and feelings and everything else. That's all the devil,' she said.
Speaking out on Saturday, Court's husband Barrymore Court said 'there should be no thought of changing the name'.
He claimed his wife 'never made the statement that transgender children being of the devil [sic]'.
'I suggest Billie Jean first check her facts before making allegations against my wife,' he told the Sydney Morning Herald.
'We have reputable sources review all her press releases and interviews and cannot trace these remarks back to Margaret.'
Mr Court went on to say his wife always shared an amiable relationship with King both on and off the court.
'Margaret always admired Billie Jean as her number one opponent and often praised her ability,' he said.
King, who is openly gay, previously said she hoped Margaret Court would attend the Australian Open so the pair could discuss the issue face-to-face.
'I was looking forward to seeing her, we usually sit together… we usually have lunch,' King said.
Court however says she will not attend event, telling organisers she would instead go 'crabbing' with her family.
King said she was one of the main 'proponents' of the court being named in honour of Court in the first place.
'When Rocket, Rod Laver, got given the arena, I said 'what are you going to do for Margaret?' the 74-year-old said.
'But I think it's its really important, if you're going to have your name on anything, that you're hospitable, inclusive, you're opening arms to everyone that comes to a public facility.
'If you were talking about indigenous people, Jews or any other people, I can't imagine the public would want to have her name on something.'
She said she wouldn't be openly encouraging others to boycott playing on the court, but asks they consider it.
Ms Navratilova recently told the New York Times she wouldn't play on the court, but doubted current players would make the decision.
In May, Court remarked 'tennis is full of lesbians', claimed transgender children were the result of parents who 'don't care' and related non-heterosexual thinking as the work of Nazis, communists and the Devil.
'God's got so much in there about the mind how it affects us, affects our emotions, our feelings, you can think 'oh I'm a boy' and it'll affect your emotions and feelings, and everything else and so that's all the Devil,' she told the Daily Telegraph.
'That's what Hitler did, that's what Communism did, got the mind of the children. And it's a whole plot in our nation and in the nations of the world to get the minds of the children.'
