One thing to keep in mind is that ALL generators consume fuel based on the (Watts) power they produce.
While larger sized generators do consume relatively more fuel at low power than a generator that is smaller near it's maximum.
Remember a generator is a device that transforms mechanical power from a power-plant (engine typically) into electrical power.
1 HP mechanical is 746 Watts (US). The efficiency will be less than 100 percent of course. The only difference between a large sized generator and a large sized as far as fuel consumption is the additional frictional loads of the mechanism.
Most are fairly efficient actually.

All this being said, I would never consider anything less than 5000 watts for home use. The smaller ones are fine for camping, but 2000 watts is very small for a number of other things than your pump.

Remember you are buying flexibility (options for unseen things that might pop up).

Really a 6000 to 7000 watt generator (around 10 to 15 HP engine) will be even better. Also the larger generator have other features such as regulation (really nice, required for things like electronics).

While 2000 watt gen-sets are nice for camping and intermittent use (perhaps) in outdoor functions, it's just too small for ANY kind of sustained use.

One final thought, engine life will be much shorter if you are loading the generator near it's maximum.
You wouldn't expect to have a car last long if you ran it at 120 MPH right ? Even if the speedometer goes to 120.

I have installed/specified a many a Gen-Set both personally and professionally ( an Electrical Engineer/Designer), and unless you want it for this one application only (water well) then your money would be better spent on something that has maximum versatility .