I don't know that there are special "names" for the seats, but who sits where is really a matter of personal preference. I only soloed our TI on its maiden/shakedown voyage on a pond in Delaware. Since hauling it down to Florida, I've always had at least one crew member along on every trip.
When using it as a kayak (main hull only), I prefer the front seat -- but any time we're sailing, I prefer the rear seat, as it is much more comfortable keeping an eye on the sail and the Windex on the top of the mast from there. It's also much easier for the crew do "mobile ballast" duty up front - moving from the seat onto the windward tramp as needed.