From the “Reilly” Wiki:
“It is usually anglicised as Reilly, Riley and O’Reilly. The original form of the name, Ó Raghallaigh, denotes “from/of Raghallach”, the name Raghallach thought to be derived from the compounds ragh (meaning “race”) and ceallach (meaning “sociable”).
The Ó Raghallaigh family were part of the Connachta, with the eponymous Raghallach said to have died at the Battle of Clontarf in 1014. The family became the kingsof East Breifne, modern-day County Cavan and County Longford.
The name is common and widespread throughout Ireland, ranked 8th most common in 1890 and 11th in 1996.”