while I doubt we are going to see the Cat forklift name go away any time soon, I have to admit the title of the thread got me to look (and they dropped the 'Caterpillar Forklift 'name a few years ago, and now are just "Cat Forklift".
According to MCFA's "official history" (as best as I can remember) MCFA was created because Mitsubishi had good manufacturing facilities, and Caterpillar had a "stronger" dealer network (I take that to mean that Caterpillar dealers, for the most part, had more capital than most Mitsubishi forklift dealers, and after all, Caterpillar dirt equipment dealers sell and finance a lot more expensive machines than most "heart of the line" forklift dealers). Caterpillar dirt equipment dealers employees usually saw the forklift business to be the companies "red headed step child" [more headaches and less profit than the dirt side].
Over 10 years ago, MCFA started what they call "1b2c" [one business, two channels] as their long term program to assist dealers in consolidation, where both brands would eventually be represented in any given geographic area by the same company (and as such would reduce 'cut-throat price' selling of the same product and services). In this area, the {current} Cat Forklift dealer is not owned by the Caterpillar dirt equipment dealer, and the Caterpillar Dirt dealer now owns the Hyster forklift dealership.