I pretty much call the style the Kauhava style, with horsehead, or without.
Will point out the little Lap knife of mine has a blade never intended for the Kauhava style, but was produced by one of the elder Kauhava master smiths, Altti Kankaanpää.
He shows up in a youtube video of several famous puukkoseppa working on a giant display Kauhava style puukko for the museum. Altti was almost 80yrs old when this still was taken at same time as the video put together showing them all building the giant Kauhava puukko, he is the one with ball cap and black jacket. They were using the giant calipers ratioed to small calipers used to measure a small normal puukko.

Here is a great older video (old film clip, actually) showing the semi-production Kauhava puukko being made, start to finish, in 14mins. These shops were formerly all over the region, puukko often marked with war of independence dates, Winter War dates, or with the flag of Finlandia. Generally for the tourist trade which came with the railroad, and never stopped.
https://www.youtube.com/watch?v=CsXmyKhIoAIIt is a truly great video of a great old smith making the puukko as they had been since the 1800s, again, in his very old shop established by his grandfather, very primitive production machinery designed to take advantage of power sources past human powered, again, much of this came with the railroad.