I've always referred to it as a compounding transformer, but I don't know what Kohler called it. Thinking about it further, I think Kohler would have referred to it just by it's part number, which has to be looked up based on the set's spec number.

It functions more as a current transformer. The two heavy windings are not across the 240 volt output, rather they are in series with it such that all load current passes through the transformer. These windings have few turns. The other winding has many turns. In this way, the heavy load current is dropped to a few amperes for the rectifier and auxiliary field winding, but they are always proportional to each other. Thus, as load increases, so too does excitation, such that output voltage is held practically constant across the load range.

Keith