The official name is "Medic [number]" So, for radio callsign, paperwork, documentation, it's Medic 31, or whichever truck you're on. The BLS crews are all numbered, starting off with a letter designation standing for their station. ex: "Kilo-74".
On the radio, numbers are typically all that's used. unfortunately, people aren't bright enough to figure out to not have a "November 31" on the same day you have a "Medic 31" on.
Other than that, 'Get in the truck.'