I was wondering if anyone could identify the name of this chess piece design, or possibly the name of its designer? It's obviously not the standard Staunton set.
It’s not exact match, but it’s possible that your set is what is called a St.George-style set.
Take a look at this Wikipedia image from the Staunton page: https://en.m.wikipedia.org/wiki/Staunton_chess_set#/media/File%3AChess_set_4o06.jpg
The way the kings, bishops, queens and pawns are built, in comparison with your set and the image above, are very similar. The rooks and knights are not exact nor are the dimensions the same. I would suspect that what you have is a variation and/or modernized design of the St.George-style chess set, such as a mesh with the Staunton perhaps.
Here’s a small article about the St,George-style that I found: http://www.chess-museum.com/st-george-chessmen.html