The name Mcallister, of Scottish origin, is derived from the Gaelic 'Mac Alisdair', meaning 'son of Alexander'. It's a surname that has been anglicized over time and now also used as a given name. The popularity of Mcallister as a first name is relatively recent, with its usage becoming more common in the latter half of the 20th century.
"From 2000 to 2006, there were eleven babies named McAllister."