What happens when a 120v 15A AC motor is connected to a 220V supply?
In case this is a destruction, what should be the power rating of a converter that is to be used?
It's very possible that it will be damaged. Most probably on its starts, where there is a higher current drawn. If not it will run at higher speed with higher current and so it will overheat. It may get hotter and hotter to finally burns.
You will need a transformer with 2:1 ratio (240V / 120V) and power of 1.8kVA (120*15). Remember to also specify the frequency when you will buy the transformer!