There are 3 main mfrs of single phase OUTPUT VFDs, one is fairly decent and is brand labeled by several other companies, but it's all the same product. The thing is, they (all of them) can ONLY work on two types of single phase motors; PSC (Permanent Split capacitor) and Shaded Pole. Those two types of motors are notoriously low starting torque so are suitable for essentially just centrifugal pumps and fans. In addition, Shaded Pole motors can be speed controlled using simpler voltage control (aka "dimmer"), so really, the single phase output VFDs are relegated to PSC motors for the most part. If your single phase motor is not PSC, you cannot use any kind of VFD on it (and have them both survive).
The other thing is, because their sales volume is a fraction of that of VFDs with 3 phase output, they cost is very high in comparison. So most of the time you will be money ahead by using a 3 phase motor and a VFD that accepts single phase input.
If you want to pursue the Single Phase OUTPUT type VFDs, the main supplier is a UK company called Invertek, their products are also sold in North America under the brand names Anacon and Bardac. The product is decent quality. The other sources are small niche players in the HVAC industry for what I call "**** fan" controllers (used to balance air flow in bathroom vent fans of large HVAC installations), I can't remember their names because they really are not industrial quality products so I never deal with them.