According to John J. Marshall, this street takes its name from Thomas Verner who was the last sovereign of the Old Corporation of Belfast from 1841–1842: The first citizen of Belfast was then referred to as the mayor of the city. During the period 1846 to 1856 Verner acted as receiver for the Donegall Estate (he was dismissed as receiver in 1855) and agent for Lord Donegall. He played a key role in seeing through the sale of Belfast. He was the nephew of Lord Donegall and the son-in-law of Sir Edward May.
"Was named after Thomas Verner, Jr,, His father, Thomas, Sr,, was Collector of Excise at Belfast. His son, Thomas, Jr,, was receiver of rents for the Marquis of Donegall, and also one of the originators of the Cavehill Railway. He was the last "Sovereign" of Belfast under the old regime. When the first elections of municipal corporations under the Irish Corporation Act of 1841 were held in 1842, Thomas Vemer was an unsuccessful candidate for a seat in the first Town Council" (John J. Marshall, Belfast Telegraph, 19/02/1941).
However, the name was given as early as 1815, which does not seem to be compatible with Marshall's explanation. Verner Jr would have been 19 years old at this time. It therefore seems more likely that it honours Thomas Verner Sr.