This name is also used as an Anglicized form of Irish Ailbhe.
This name was popular throughout the English-speaking world in the early 20th century. It staged a comeback in the early 21st century, returning to the American top ten in 2017.
A famous bearer of the surname was James Madison (1751-1836), one of the authors of the American constitution who later served as president (and after whom Madison Avenue was named).
This name is also common for girls in Estonia, though a connection to the English-language name is uncertain.