It depends on the area. Baby Jesus in Milan, Santa in my area which is 25 miles east of Milan. In my area and in Sicily there's also St. Lucia on Dec 13th. If you go to Rome, there's also the Befana on Jan 6th.
Santa (well, Gwiazdor, but it's essentialy the same thing), Baby Jesus, a shooting star, Krasnoludek, an angel...
Santa dominates in media though, since he's western and ****.