It had been reported the pair was considering a traditional Scottish name for the newborn, who was welcomed into the world on Sunday night (07Feb16), with Freya the best guess.
However, a family friend has now confirmed the little girl's moniker to the Daily Mail newspaper.
The speculation about the name comes after Andy's grandmother Ellen told the publication she had received a phone call from her grandson confirming the birth.
"Andy phoned and said, 'Congratulations, you're a great-granny'," she said. "He told me the baby was 8lb 10oz when she was born. It's wonderful news. We watched him in the Australian Open final and I think he just wanted to come home.
"I don't really know about her name yet but I hope we'll see them all soon. I'll be looking forward to a cuddle."
Andy's mother Judy Murray's mother Shirley Erskine added that Andy and Kim had "sent a text around all the family" after their daughter was born, and did not know they were expecting a little girl.
Former Wimbledon champion Andy married his longtime partner in his hometown of Dunblane, Scotland in April, 2015 and reports of the pregnancy emerged in August (15).
He recently spoke of how becoming a father will change his relationship with tennis, telling reporters at the Australian Open tournament, "It's a big change for me and my wife, but that's the current priority and I'll see after that... I have no idea how that will change things. I still love tennis."
Andy had planned to exit the competition if Kim went into labour.