In 1857 Lady Harriet Chichester, the only daughter of the 3rd Marquess of Donegall married Anthony Ashley-Cooper, then styled Lord Ashley. He subsequently became the 8th Earl of Shaftesbury in 1885 and inherited Belfast Castle. He died in 1886 (the year that this street was named) and was succeeded by his son, also called Anthony.
"Resolved that on the application of the residents of the neighbourhood and the owners of property, the portion of Great Victoria Street from Albion Street to Wesley Place and the new buildings from Pakenham Place to Donegall Pass, and the houses known as Oxford Buildings be named Shaftesbury Square. that Dr S. B. Coates be informed thereof" (2nd December 1886).