Agree with all of what Jraef states.
As for..."What would a motor shop actually 'do' to tell?"
Here's the sequence of inspecting a polyphase motor having no nameplate.
1. The very first tool a technician in a motor shop would use is a "megger" to
determine if the apparatus is grounded.
You can also use a multi-meter, but a megger is actually applying potential to the
stator winding (typically 500 or 1000 volts). A VOM can't do that.
2. The next subtle act would be in physically turning the shaft to learn whether
the shaft of the motor even turns.
(No further electrical testing takes place if shaft does not rotate.
At this point it becomes a candidate for dismantling if the item is even worth repair.)
3. If the motor is not grounded and the output shaft rotates freely, the next step is to
determine if the motor has a functioning circuit. This can be accomplished using an ohm
meter, but in an adequately equipped motor repair facility, typically a device called a
"surge tester" is used. Again, this device applies potential to the motor winding and compares
each phase of the stator winding to verify a functioning 3 phase circuit.
To compare the windings using an ohm meter in some cases may require that the meter can
measure very low resistances. Not all off-the-shelf multi-meters have the ability to measure
very low resistances. (Resistances below 1 ohm.)
4. If the above electrical tests all pass, the next step would be to apply power to the motor.
The lowest output of a test panel is applied first. For a low voltage NEMA frame motor
the voltage applied first is typically 230 volts... but can be lower if the supply has that option.
Upon applying power, the reaction of the motor is observed and operating current is measured
and compared between the three phases of potential.
If the motor is connected for 230 volts, upon applying power to the device, it will have a sharp
snap, or jump as it quickly comes up to its no-load speed.
If the motor has a somewhat "sleepy", sluggish start as it ramps up in speed, the motor is
suspected of being connected for 460 volts. The current drawn or indicated will also help
confirm this.
Note: A competent motor repair facility would not release a rewound motor without a name plate.
Additional steps required to determine the motor's frame size and horse power output are pursued to gain
data for affixing a new nameplate.
Here's a fun fact related to NEMA frame motors seldom mentioned in motor conversations.
If you take the first two numbers of a motor frame, and divide that by 4, it provides the foot
to shaft center line dimension.
John