She is suing the newspaper's publisher for breach of privacy and copyright infringement after it reproduced parts of a letter sent to her father in 2018.
The publisher, which denies the claims, argued her friends could be witnesses, saying the letter was first referenced in their interview.
Meghan said they had a privacy "right".
The application to maintain her friends' anonymity was heard at London's High Court, as part of the duchess's legal action against Associated Newspapers Limited.
Neither Meghan nor Prince Harry attended the latest hearing on Wednesday.
In an article in People magazine in February 2019, five friends anonymously spoke out against the bullying Meghan said she had faced from Britain's tabloid media.
They have only been identified in confidential court documents.
In a witness statement submitted to the High Court, the duchess said Associated Newspapers, the publisher of the Mail on Sunday, was "threatening to publish the names of five women".
"Each of these women is a private citizen, young mother, and each has a basic right to privacy," she said.
"Both the Mail on Sunday and the court system have their names on a confidential schedule, but for the Mail on Sunday to expose them in the public domain for no reason other than clickbait and commercial gain is vicious and poses a threat to their emotional and mental wellbeing.
"The Mail on Sunday is playing a media game with real lives."
In court documents for the hearing, Meghan's lawyers argued the friends have a right to anonymity both as confidential journalistic sources and under their own privacy rights.
Justin Rushbrooke QC, representing the duchess, said forcing her to disclose their identities would be "an unacceptably high price" to pay for pursuing her legal action against the newspaper.
Lawyers for Associated Newspapers Limited are resisting the application to keep their identities secret, claiming the duchess's friends brought the letter into the public domain when it was referred to for the first time in the People interview.
In written submissions, Antony White QC, acting for the publisher, said the friends were "important potential witnesses on a key issue".
"Reporting these matters without referring to names would be a heavy curtailment of the media's and the defendant's entitlement to report this case and the public's right to know about it," he said.
"No friend's oral evidence could be fully and properly reported because full reporting might identify her, especially as there has already been media speculation as to their identities."
Mr Justice Warby said he would give his decision on the duchess's application in writing at a later date.
The Duke and Duchess of Sussex are now based in California, having stepped back as senior royals at the end of March.
Meghan is seeking damages, which she has said will be donated to an anti-bullying charity, from Associated Newspapers for alleged misuse of private information, copyright infringement and breach of the Data Protection Act.
Associated Newspapers denies the allegations.
Following a preliminary hearing in May, the judge struck out parts of Meghan's claim against the publisher, including allegations that it acted "dishonestly" by leaving out certain passages of the letter from her father.
He also dismissed Meghan's claims that the publisher deliberately "stirred up" issues between Meghan and her father, and that it had an "agenda" of publishing intrusive or offensive stories about her.