Notice that the first two guns have stocks that were colored/painted black. When the "Broen Bess" as adopted it was the first British musket with no black applied to the stock. Hence, to the common soldier it was the "brown gun" In common English - not Shakespear, that was said as "brown bess". Brown meant just what you'd think - BROWN, not colored/painted black. And, although today's Englishman may not be aware, "bess" was from the old German word for "gun". Had nothing to do with any woman's name. With all respect to our British members here, in America we have kept some of these obsolete words in the language of Southern blacks. Their enslaved families learned 16th or 17th Century English as spoken by rural English, the Southern plantation owners. They did NOT speak as Shakespeare wrote. To them a gun was something like a "bess", and to shoot at someone was then, and still was when I was young, to "buss" them. I recall in the 1970's a Detroit newspaper quoting a black resident sying something like "...he buss at me, I buss back". At that time I spoke with a Caucasian man from Alabama who said "I know what that means"
So . . . just don't "buss" at your friends. And do not look for the term "Brown Bess" in any fine English literature of the 17th Century.