Following his first-round win over Andrey Kuznetsov at the French Open, Murray said: “I don't see why anyone has a problem with two people who love each other getting married. “For players to be in a position where you're in a slam and boycotting playing on the court, I think would potentially cause a lot of issues.
“So I think if something was going to be happen and the players come to an agreement, if they think the name should be changed or whatever, that should be decided before the event starts.
Court, 74, became a Pentecostal Christian minister after a glittering career in the sport, during which she won 24 Grand Slam singles titles, including a record 11 at the Australian Open.
She is a vocal critic of LGBT rights and caused controversy last week when she said that she would not fly with the Australian airline Qantas, because of its support for same-sex marriage.
A number of current tennis players expressed their disapproval of her comments, including Andy Murray.