Rumour or legend has it that the great Jimmy Weir commented on how they were playing in a game saying " They are fighting like Warriors" and that was how it came about.
However from Google .......
The club was formed via a breakaway group from a local junior team called Heather Rangers in 1884. They played at two other local grounds, Tryst Park and Goschen Park, before settling down at Ochilview in 1890. The nickname 'The Warriors', has been used since at least 1887 but the actual origins of the name are lost.