"The origin of the name Ann Street is rather obscure. It suits the position of Catharine Street, in which the first Linen Hall was built in 1739; but that Linen Hall was referred to in 1754 as in Ann Street, and it certainly was so. If the streets be identical, the name has been changed in the interval between 1739 and 1754 (George Benn, A History of the Town of Belfast, vol. i, 1877, p. 529).
N.B. It seems that this is due to a confusion rather than a renaming of the street. In the 18th century Catherine Street was an alternative name for Caddell's Entry, a side-street on the north side of High Street, probably because Catherine Caddell held a lease for premises there.
Ann Street existed at least as early as 1685 when it was marked on Phillips' map, but unnamed. It was recorded as Anne Street in 1712. It was also known as Back Street because High Street was considered the front street. Mary Lowry in her book states that it was called after Anne, Lady Donegall. It is included in the list of streets in the Belfast Directory 1831-1832.
According to the Irish Historic Towns Atlas, vol. xii, Belfast’s first Linen Hall was built in Cooney's Court, part of Ann Street, and opened in 1739. The artillery barracks built in 1737 were also in Ann Street. It was from these barracks that the heavy guns used by the troops at the Battle of Ballynahinch (1798) were supplied. It is thought that the eight small ships’ cannons used by the United Irishmen were brought after they had been defeated.
Ann Street also had the first regular theatre in Belfast. From newspaper adverts there would seem to have been a “modest” playhouse in the street called “The Vaults”. It was used until a new theatre was built in Rosemary Lane (now Street) in 1784 (John J Marshall, Belfast Telegraph, 30/12/1940).