The street was originally named as Barrack Street as it was close to the former Royal Barracks. The section closest to Queen Street was known as Tighe Street, but previously known as the Gravel Walk up to circa 1780. Both streets were amalgamated and renamed Benburb Street in 1890. It was named for the Battle of Benburb in County Armagh in 1646.
The Baptist Church on Grosvenor Road was designed in 1859 by Carmichael and Jones, a partnership formed by Hugh Carmichael and Alfred Gresham Jones in 1854.