From Nigel Olifaunt, Lord Glenvarloch, hero of 'The Fortunes of Nigel' (1822) by Sir Walter Scott (John J. Marshall - Origin of Some of Belfast's Street-Names, p. 14). Note the discrepancy in spelling.
Unlike some of the other Scott-related names like Woodstock, Ardenvohr and Clanchattan, this name seems to have been applied directly to the street and there was no earlier house or terrace named Glenvarlock.
‘Glenvarnock Street’ (sic). Resolved that on the application of the owner, Mr J. D. Dunlop, new streets on his property situate off Castlereagh Road be named ‘Glenvarnock Street’, ‘Lambourne Street’, 'Wayland Street' and ‘Quinton Street’ and that he be requested to submit another name instead of Brenda Street, as there is already a street of almost similar name in the city. TIC: 31st January 1900.