Rutland is a ceremonial county in the East Midlands of England. From 1974 to 1997 it was incorporated into Leicestershire, but in 1997 it was restored as a county with its own county council.
Given that there are several streets in this area which can be linked with British Unionist politicians, namely Hatfield Street, Farnham Street and Balfour Avenue, it is likely that Rutland Street also belongs to this group and is named after one of the holders of the title "Duke of Rutland", who were politicians in the 19th century. For example, Lord John Manners, 7th Duke of Rutland, was Postmaster General in the Conservative government led by the Marquess of Salisbury, 1885-86.
"On the application of the owners, your committee have named ... four new streets off Ormeau Road Hatfield Street, Farnham Street, Rutland Street, and Balfour Avenue respectively...". (Belfast News-Letter - Thursday 02 October 1890)