Named 'Archibald' by Lands and Lairds1 but 'Joseph' by Burke2.
Footnotes
[1] Lands and Lairds of Larbert and Dunipace Parishs, John C. Gibson, Glasgow (1908); Bruce of Stenhouse, pages 15-27
[2] Burke's Peerage, 99th Edition, by John Burke and Sir Bernard Burke, 1949; Bruce of Stenhouse, pages 281-283