Young Kevin is named after the mayor and Maggie's own son, who died of spina bifida in 1981 at the age of 2.
The mayor talked about that at a news conference Tuesday.
"The death of child always stays with you. It doesn't matter what age a child is. As a parent, it always stays with you. So that's really something special, naming her third child Kevin," Mayor Daley said.
The mayor added that both mother and son are healthy and doing well.