It seems likely that this street was named after one of the holders of the title "Earl of Onslow", a title in the Peerage of the united Kingdom created in 1801 and still in existence. This argument is strengthened by the presence of Haddington Gardens and Shelbourne Road in the same neighbourhood. Haddington (East Lothian, Scotland) and Shelburne (sic, Co. Wexford, Ireland) are unrelated geographically but are also names of earldoms. The title "Earl of Onslow" relates to Onslow near Shrewsbury in Shropshire, England. Onslow Hall (demolished) was once the residence of the Onslow family, but the seat of the current Earl of Onslow is Clandon Park in Surrey.
"Resolved – That the name Onslow Parade be approved for a new street on the property of Messrs. H. & J. Martin, Ltd., situated off Cregagh Road". (17th February 1931).