In his video appearance before Court's on-court presentation on Monday,McEnroe took aim at Court for her history of homophobic,racist and transphobic views.
"There's only one thing longer than the list of Margaret Court's tennis achievements,"he said.
"It's her list of offensive and homophobic statements."
Navratilova wrote that Court was not on"the right side of history".
"When airports,buildings,streets or stadiums are named after particular people,it is done,or at least should be done,to honour exceptional human beings — our heroes,"she wrote.
"Think Muhammad Ali,Nelson Mandela,Martin Luther King,Billie Jean King,Rod Laver,Rosa Parks. Would it not be appropriate if the Staples Center were renamed as a tribute to Kobe Bryant?
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"Such luminaries excelled in their fields and transcended them;they made a positive contribution to mankind;they led by example. And,perhaps most of all,they were on the right side of history.
"But Margaret Court does not belong in that company or category. Nobody disputes her achievements on the tennis court,and her place in the sport’s history remains as distinguished as it gets.
"So,it pains me to say this but Margaret Court Arena must be renamed.
"As a worthy replacement,my vote goes to Evonne Goolagong. Evonne is the embodiment of what a role model or hero truly is."
Margaret Court has been contacted for comment.