Owner: Mr Shillington, eight new streets situate off Broadway be named Benburb Street, Ebor Street, Kilburn Street, Lecale Street, Moltke Street, Rockview Street, Tavanagh Street and Glenmachan Street. Minutes TIC, 25th May 1898. Benburb Street features in the 1900 The Belfast And Province Of Ulster Directory as above.
The Shillington family had a connection with Benburb with some members of the family living there for a time which would suggest this is how Benburb Street got its name.