Australian tennis Open venue Margaret Court Arena will not be renamed despite the 24-time Grand Slam champion's opposition to same-sex marriage.
The 74 year old Australian, now a Christian pastor, says she will not fly on Qantas "where possible" in protest of its support of same-sex marriage.
Tennis Australia stated that her personal views "are her own".
Grand Slam winners Martina Navratilova and Billie Jean King, who are both gay, have previously criticised Court.
The venue was originally called Show Court One when it opened in 1988 before it was renamed in 2003 in tribute to the multiple Grand Slam winner.
The Margaret Court Arena also hosts other sporting events and concerts.
Court expressed her views in an open letter to the national airline published in The West Australian newspaper.
She said: "I am disappointed that Qantas has become an active promoter for same-sex marriage.
"I believe in marriage as a union between a man and a woman as stated in the Bible.
"Your statement leaves me no option but to use other airlines where possible for my extensive travelling."
American singer Ryan Adams, who is playing at the arena on Friday, tweeted: "Hey Margaret Court, a PAGAN who STRONGLY SUPPORTS marriage equality (get a prenup tho) will play the arena named for you tomorrow."
And Tom Steinfort, a senior correspondent for Nine News in Australia, tweeted: "I'll never set foot in Margaret Court Arena again because of this."
Peter FitzSimons, chairman of Australia's Republican Movement, called for the venue to be renamed in a piece for the Sydney Morning Herald.
Tennis Australia tweeted a response: "As a legend of the sport, we respect Margaret Court's achievements in tennis and her unmatched playing record. Her personal views are her own, and do not align with Tennis Australia's values of equality, inclusion and diversity."
Court won 11 Australian Open singles titles in the 1960s and 1970s, five French Opens, five US Opens and three Wimbledon crowns.