VFD is designed for use on standard motors. So, most applications and selection is mostly straightforward with a little knowhow and experience. If in doubt, refer to your supplier for guidance.
Occasionally, there will be selection considerations applying to certain applications or installations as outlined briefly in other posts e.g. high load at low speeds, long cable runs to motor (high capacitance), super synchronous operation above normal motor speed etc., so seek guidance on these. This normally ends with a standard VFD and motor and extra filters or chokes if needed. So called VFD motors are normally standard motors selected and nameplated for the application, or have an electric cooling fan in place of shaft mounted. Larger motors may use a standard winding in a larger frame to help cooling at lower speeds, for example.
I have seen only rare problems in many 1000s of applications. Notable problems have occurred with 'non-standard' motors such as: integral fan motors, submersible, high speed exhibiting problems / failure because of such reasons like lower cooling capacity, lower insulation levels, no interturn insulating paper for example. So, if you have special requirements or motors, check with VFD and motor supplier for compatibility to your needs to avoid problems later on.