We wonder if Lily is a fan of the HBO series Girls and decided to name her new arrival after her favourite character - just a thought.
"Marnie is a real cutie," a friend of the Cooper clan allegedly told the tabloid. "Sam and Lily are ecstatic about adding another girl to the family."
The couple have yet to confirm the birth, BUT Lily did take to Twitter, after receiving endless messages of congratulations, to thank her well-wishers for their support.
Quite overwhelmed by all the well wishing going on. THANKYOU everybody x x x
- lilyrosecooper (@lilyrosecooper) January 10, 2013
Lily's certainly a trend-setter when it comes to traditional baby names, but will we see a surge in popularity of her choice for baby number two? Could it be a contender for the Royal baby, perhaps?
The singer is certainly in good company, joining the likes of Claire Danes, Sienna Miller and Megan Fox in the new mum club.