Good news, I found an explanation for Pawniard and Bisharp! Pawniard is an ashigaru, a japanese foot soldier that serves under a samurai characterized by their rounded helmets, while Bisharp is the samurai itself. It would explain why Bisharp are described as commanding armies of them. The chess puns in the English names are probably just an attempt to localize them, but it does make some sense since pawns can be promoted into bishops. What do you think?
Well, there is a chess pun in the Japanese too, because Pawniard’s Japanese name references the word for a game piece (koma), so it still seems likely to me that they were influenced by the appearance of pawns in European chess. But it does make a lot of sense – maybe someone at Game Freak thought that pawns in Shogi could be imagined as ashigaru, and then made a connection with the shape of European pawns?