The Duke and Duchess of Sussex issued legal warnings against the BBC after a report claimed the couple had not asked the queen’s permission before naming their baby Lilibet.
The BBC’s royal correspondent quoted a palace source saying the monarch was “never asked” about the use of her nickname.
But Harry and Meghan insisted they had sought permission and accused the BBC of libel.
“The article is false and defamatory, and the allegations within it should not be repeated,” lawyers for the couple said.
A representative for Harry and Meghan said the duke had spoken to the queen and would not have chosen the name had she not approved.
“In fact, his grandmother was the first family member he called,” the representative said.
“During that conversation, he shared their hope of naming their daughter Lilibet in her honour.”
Congratulations to The Duke and Duchess of Sussex on the birth of Lilibet Diana! The Queen, The Prince of Wales and The Duchess of Cornwall and The Duke and Duchess of Cambridge are delighted with the news.
Harry and Meghan announced on Sunday that their daughter would be named Lilibet Diana Mountbatten-Windsor.
Reports are rife of a rift in the family since the couple said last year that they would step back from royal duties.
Tension reached boiling point after an interview with Oprah Winfrey in March, during which the pair said they had suffered racism within the royal family.
The legal threat is the latest clash between the duke and duchess and the British media.
In March, The Mail on Sunday was ordered to print a front-page statement after losing a privacy case against Meghan over the publication of private letters.
Harry earlier won “substantial damages” and an apology from the same newspaper over an article that claimed he had turned his back on the military after stepping down as a senior royal.
The pair last year said they would no longer engage with the Mail, or tabloid rivals the Sun, Mirror and Express, accusing them of false and invasive coverage.