According to Phoenix and Rasmussen in the book Folktown, Marquis Street originally known as Ferguson's Lane after the family of Sir Samuel Ferguson, the Belfast-born lawyer and poet whose father owned a tanyard there. They indicate the name was changed in honour of the Marquis of Donegall. According to these authors the street is first shown in a 1791 map. It is first named in the Belfast Street Directory (1813).
Probably named after the 2nd Marquess of Donegall. However, the street existed as early as 1791, so a link with the 1st Marquess is also possible, especially as the title of Marquess of Donegall was created in this year.