Mel B has named her daughter Madison Brown Belafonte.
Mel has also confirmed all is well with her baby, adding: "The doctor said the baby is really, really healthy."
The 36-year-old singer - who also has four-year-old daughter Angel from her relationship with Eddie Murphy - confirmed Phoenix would be picking the name and did not want her to make a quick decision on Saturday (07.09.11).
She wrote on twitter: "Phoenix my daughter is still deciding our babies name, i don't wanna rush her, it will be soon! (sic)"
Since the delivery, Mel has been enjoying no longer being pregnant as it means she can once again enjoy her favourite hot beverage, a soy late.
She tweeted: "can't beat a large hot vanilla soy latte with an extra shot, bring it!!! i missed them for 9 months (sic)"
She has also been planning play dates for her newborn daughter and Denise Richard's three-month-old adopted daughter Eloise.
Denise sent a message on twitter to Mel saying: "@OfficialMelB congrats mama! Can't wait to meet her!!!...xo"
To which Mel replied: "@DENISE_RICHARDS thank you sweet heart, play dates for sure xxxx (sic)"