Welcome to the CCF, Marcus. IMHO, this c/s is too large to be that of a silversmith. It's more likely to be that of a blacksmith, tinsmith or other craftsman. The stamp appears to have been too large for the coin, and the name, probably a W.A. BAKER, was partially stamped on both sides, a continuation. I've seen this practiced upon many a coin.
The W was most likely a William, but there are other possibilities, of course. Sadly, the surname, Baker, is quite common. Doing a cursory search of some early directories, I found a minimum of ten prospects by the name of W.A. BAKER. To my eye, the letter style suggests a relatively early counterstamping; done between 1810-1860 ... an educated guess.
Brunk didn't list a W.A. BAKER c/s in 2004, his last work. That said, unlisted counterstamps are more the rule than an exception, nowadays. That's part of the appeal for me, and I regard this study as "the final frontier of numismatics." The mysteries, yet to be solved, are what appeal to me. Brunk, with the aid of many contributors, did a great job of pinning down attributions in 1987. That said, he had to make a number of amendments seventeen years later. Attribution of counterstamps is an evolving process. The internet is helping me solve many an attribution. Yet. I tend to avoid the more common names like Smith, Jones, Baker, etc., unless other counterstamp clues are present.
On occasion, one can attribute an apparently maverick counterstamp like this Baker piece by association. Sometimes, another counterstamped coin may show a town or occupation that can lead to a match. Sometimes, the same counterstamp may be found upon a tool, a firearm or some patented product. Then too, there are times when the field can only be narrowed to two or three likely prospects.