Munroe, Monroe
Munroe, Monroe—These two names are the anglicised forms of Mac An Rothaich, a clan located in Cromarty in the North of Scotland, and descended from Donald O'Kane and his sept who went from the banks of the River Roe, in Derry, and settled at Ferindonald (Fearr an Domhnuill), in that county, hence the name of Monroe, from the River Roe in Co. Derry.
Alphabetical Index of Anglicised Surnames in Ireland
See also Woulfe’s Irish Names and Surnames
… and O'Hart's Irish Pedigrees