It’s entirely possible to run a 240-volt well pump with a generator, but only if the generator itself is capable of delivering 240 volts. Not all are. This is twice as high a voltage as found at normal electrical outlets, and is the standard voltage for larger appliances. In practice, 240 volt appliances use two 120 volt feeds, and the amperage you measured on one of your water pump wires is the same as what you’d find on the other. But you don’t add these figures when determining what size of generator you’ll need. Just take the amperage figure you measured, then multiply it by 240 volts.
In practice, however, the job of choosing a generator for a 240 volt water pump is actually very simple, since only larger generators deliver 240 volts in the first place. Even the largest household water pump requires only about 1000 watts to operate, and any generator capable of providing 240 volts that I’ve seen will be larger than this. At my house, for instance, a 3500 watt generator is enough to power the 240 volt water pump in our well, some basic lighting and the fridge and freezer that kicks on or off as controlled by their thermostats.