Technically it's possible to make a 120V single phase VFD and run a normal motor, but the application is not practical. Such devices exist, but they really don't work very well, are expensive, and have very limited application.
The better options are:
A 120V single phase input VFD and a 3 phase 240V motor up to about 1/2 HP.
A 240 single phase input VFD and a 240V 3 phase motor up to about 5 HP
A brushed DC motor and controller
A Brushless DC Motor and controller.