The primary origin is from the Gaelic odhar, meaning "dark", "dun".

The first recorded evidence of the name in Ulster is of those who came from Scotland with Sir Hugh Montgomery in 1606 to settle in North Down on lands ceded by the O'Neill family.

According to Bell, the earliest record of the name in Ireland is that of a family in County Tyrone in 1655.

Historian Edward MacLysaght suggests that the name in Scotland derives from the parish of Urr in Kirkcudbrightshire.

A tradition of some of the Orrs in Northern Ireland has it that they were descended from outlawed brothers whose original family name was McLean; they crossed this river and then made their way by boat to Donaghadee in County Down in the early 17th century.