Motor type?

I can't think of anything on the ID plate that is missing.
What type of motor do you think you need for your VFD?

 

Your motor ID plate says it's a 'Single Phase Asynchronous Motor for Air conditioning'.
Typically, an Asynchronous Motor is a slip-ring rotor, or Squirrel-cage rotor.
So it's not Split Cap or Shaded Pole.
The other issue is whether or not your VFD is single-phase or three-phase.
I think you need to do some Googling.
I'd start with the manufacturer of the VFD, and start checking is's specs and recommended
drive motor.
Good luck.

 

Another issue you need to be concerned with: when using a motor with a VFD is cooling the motor. Most motors used with VFD's are Inverter rated/duty. This means theyhave higher winding insulation rating and when operating at a reduced speed the integral fan moves enough air to cool the motor.
My experience with VFD have been to convert single phase to 3 phase. I used them to run air compressors and pumps allowing a soft (slow speed) start. the 3 phase motors are a lot smaller physically for the same horsepower.

I could't make out the diagram as to see if there was an internal centrifugal switch to disconnect the capacitor once the motor is up to speed. (Capacitor start). In that case, the motor may not get up to speed to activate the switch resulting in overheating the start winding.

If the capacitor is in the circuit all the time it is a capacitor- run motor.

In cooling applications it's sometimes easier to use controlled louvers rather than change the speed of the blower.