So a few things to clarify, it is one thing change the wiring on the machine from 120 to 240V single phase if designed to do so. But a whole different proposition changing out the motor to 3 phase and adding a VFD. There are a multitude of factors that determine the load requirements and electrical sizing of the socket, and the requirements of the equipment you plan to use. Looking at the Hp alone, well that can be anything depending on the actual current being drawn at the rated voltage, what load it is operated under, and for how long. You often see vacuums rated 4-5Hp, but plug into 120VAC 15A sockets, the real continuous Hp/current is much lower. A VFD on the other hand can draw upwards of 200% of the motor amperage for up to a minute, so the maximum size 120VAC VFD is around 1.5 Hp and this requires a 20A plug/breaker. As other's mentioned, most 120VAC sockets are 15A, so trying to run a 2 Hp motor off of that is not wise. The running Hp/current under no load is less, but current and resistance is what cause heating in the wire. Use a smaller wire at a higher current = more heat and eventually damage and possibly fire.
Breakers are designed to protect the wiring, but the assumption is you are not overloading them based on the socket/plug rating. Breakers are also designed with different trip curves, depending on the age and wiring, it may not be working at 100% of spec. Wiring in a house and also appliances have a safety margin built but there may be some de-rating based on the the wire ratings and associated equipment. A breaker is usually designed to trip based on current over time, so you can pull higher peak currents over a specified time. The motors with very high starting currents to not trip the breaker, as long as the current quickly declines.
If you plan to go to a VFD, then you need to replace the motor and for the most part you would not be using any of the current machine controls/wiring, so a complete rebuild. The only available VFD's for 2 Hp are 240VAC, the VFD manual will usually specify a 30A breaker, it may run off of a 20A breaker if you dial down some of the VFD load parameters or have light duty use. It will run, and may be fine, but for continuous use with load I would use a 30A breaker. The circuit breaker is supposed to be sized to ~125% of the VFD full load rated input current, does not matter what the VFD is connected to.