How do you label an ON-Off-On switch then?
It is an on-off-on switch. By the description it is a double throw. But there is no reference to the number of poles.
Pole is the number of branches. A 3-phase motor uses a 3-pole contactor. Each pole is a separate switch isolated form the other pole(s) with only the mechanical lever connecting them all together. Double pole is very common, I've dealt with a few 3 and 4 pole switches.
Throw is the number of "on" positions the switch has. One or two "throws" is normal. There are a few 3-throw toggle switches (on-on-on) but they are very rare. Never seen one in person. A rotary switch has a "throw" for each detent in the switch.
The "off" in the center position is just that. Off. None of the contacts inside the switch are connected. Since nothing is connected, it isn't considered a "throw".
Most switches are "non-shorting" where a throw disconnects from one contact, passes through an "off" position (that may or may not have a detent to hold it there) before the other contact closes. There are a few rare (you have to really go looking for them) "shorting" switches where the second contact is connected before the first is released. This creates a moment where all 3 terminals (common each of the contacts) are all shorted together.