The name Maxwell has a family history from dad Eric Johnson's side -- it's his middle name and his grandmother's surname. Drew is the maiden name of Jessica's mother, Tina Simpson.
And Life & Style was first to report that the parents plan to call their baby Maxi for short.
Back in April, Simpson talked baby names to Elle magazine and promised "It's nothing shocking and nothing you'll have to add to the dictionary. Still, when people hear it they'll know … why."
Well, if the hundreds of comments on Yahoo! are any guide, J-Simp couldn’t have been more wrong.
While wishing the new mother and child well, some couldn’t help but weigh in on the choice of the name. One wrote, “Maxwell? That's like naming a boy Julie. You can call her Maxi but her license will always say MAXWELL and that is just wrong. Poor thing.”
Another wrote, “Cute name but they are going to go round and round at the school over being called Maxi pad all of her school days.”
Annie81 worried, “What is it with these people and baby names? Maxwell? It's not enough that sounds like a BOY'S name... it's going to be the source of 1000's of jokes and kids making fun of her.”
CZL noted, “Not fond of Maxwell for a girl, but since it is a family name I can see where it makes some sense.”
Commenter Allen wrote, “Maxwell? May as well named it Bob.”
Others liked it: As one wrote, “Maxwell, smart.” Loretta added, “It's still better than Blue Ivory, Apple, Rumor,etc.”
For their part, the happy parents are thrilled with baby Maxwell. Writing on Simpson's website, the couple exclaimed, “We are so grateful for the love, support and prayers we've received. This has been the greatest experience of our lives!!"
Watch Jessica Simpson talk baby names on "Ellen":