The 'LDN' star welcomed her first child with husband Sam Cooper back in November, but the couple have yet to make an official announcement about the happy occasion.
It has now been alleged in The Sun that Allen and Cooper have named their daughter Ethel Mary, with the singer's mother Alison Owen apparently confirming the news to a friend on Facebook.
Allen's only reference to the arrival of her daughter on Twitter has been to write "totes amaze" on the day of birth, followed by a message on December 5 saying: "Thank you for all the flowers and lovely messages everybody. very touching indeed. nuff luv (sic)."
Cooper announced Allen's pregnancy at their wedding reception on June 11.
They tied the knot in a "typical village" ceremony in Cranham, Gloucestershire earlier that day.
Watch Lily Allen in the video for 'LDN' below: