"Rusty's One-of-a-Kind PAW Patrol Vehicle" is not an official name yet. It may have been referenced in the storyline as such, but has not been officially named. Alternatively, it may be a name popular among fans, but has no official basis.
The short begins with an announcer (Chris Phillips) introducing Rusty's one-of-a-kind PAW Patrol vehicle. Rusty asks "Are you ready, pups?" followed by the PAW Patrol cheering in excitement. Rusty then introduces the Fire Copter 4000, a modified version of Marshall's fire truck that has helicopter wings, jet engine thrusters, and a giant claw for hard to reach rescues. He then dubs the vehicle "Rustified", to Marshall's satisfaction. The short ends with the announcer telling viewers they can watch Rusty Rivets weekdays on Nickelodeon.