Before a large amount of redevelopment in this area, there was a street called Granville Street. The street was officially named at a meeting in 1869.
"The application of Mr James Dunn for permission to name a new street off Leeson Street and Grosvenor Street “Granville Street” was granted". (3 February 1869).
The Belfast And Province Of Ulster Directory 1870 indicates people already living there as well as a section of vacant ground which goes to show the street is still being developed. It is possible Granville Street as was got its name from Granville George Leveson-Gower, 2nd Earl Granville, (11 May 1815 – 31 March 1891) who was a prominent politician in the 1860s. “Granville did succeed in re-establishing good relations with America which had been strained by the Civil War”.
https://www.gov.uk/government/history/past-foreign-secretaries/george-gower.