The baby was born Saturday night by Caesarean section in New York at Lenox Hill Hospital, EW.com reported.
Soon after the name announcement, the entertainment site said there was already a trend on Twitter under #NamesBetterThanIvyBlue.
Beyonce, 30, and 42-year-old Jay Z, whose real name is Shawn Carter, married in 2008 after six years of dating. This is their first child.
Beyonce announced her pregnancy at the MTV Music Awards in August.