This street takes its name from the nearby Rosebery Road which was called after Archibald Primrose, 5th Earl of Rosebery, who was British Prime Minister in 1894-1895. Although the title Earl of Rosebery is in the Peerage of Scotland, it refers to Roseberry Topping (note the spelling with 2 Rs), a hill in North Yorkshire near the estate of the 1st Earl's wife.
"Resolved that on the application of the Housing Committee the street between Carlingford Street and Rosebery Road be named Rosebery Gardens". (15th March 1921).