There isn't a single name for a lowered seat-stay junction. It's only a compact if the rear end of the to-tube is also lowered.

Sometimes, the lower seat-stay junction is accompanied by extension of the seat-stays to the top tube. This style also has no one name.

Why do these things? It depends on the builder. Some of it (perhaps most) is about acheiving a visually distinctive style. Sometimes, a builder may want to limit heat near the seat lug - especially with a fileted or tigged joint - to avoid distorting the seat tube. The seat tube can, and often is reamed to round - but this can be problematic for thin walled tubing.

Sometimes it is claimed that rigidity is enhanced when the stay joins the seat-tube low and then joins the top-tube several inches ahead of the seat=tube. Sometimes builders figure that they're saving a few grams by shortening the seat-stays.

Some people just like the style, especially with monostays.