Tivoli is a town in Italy, about 20 miles from Rome. It is also the name of an amusement park (Tivoli Gardens) in Copenhagen. And contrary to other comments, it is my family's name. In the past, Italians used names of towns for children who had been orphaned or what they used to call "foundling" children, especially in Sicily.
Tivoli is not used as a name in Italy. It would sound ridiculous there, since Italians don't name their kids after their cities. It's quite ugly, anyway.