Your household 120v circuit could have been tripping because there were other loads on the same circuit at the same time. To avoid that, you could do several things: Remove all other loads on the same circuit. Use a different circuit with no other loads. Lower the charge rate (which lowers the load), but I'm guessing the issue was other loads as the max charge rate on a Varg on 120v shouldn't trip a 15amp circuit with no other loads.
Note that US standards are 120v and 240v (though may still use the outdated 110v and 220v). Use 120v and 240v for your calculations. If you put a multimeter on your household NEMA5-15 outlet (your regular old household outlet), your going to see 119v - 120v (not 110v).
Per electrical codes and industry standards for household circuits, best practice is to to limit your load to 80% of circuit rating. 15amp. 120v x 15A = 1,800watt. Times .8 leaves a sustained load capability of 1,440watts. It's my understanding the Varg uses a 3,300W(3.3kW) charger, but you only get that on 240v. Using 120v limits you to half that rate, so 1,650W. There are many that would go ahead and charge at that 1,650W rate on an 1,800W household circuit. Up to the user. You'll be pulling about 14amps through that 15amp 120v circuit.
If you have a 240v circuit (or generator), you can charge at the full 3.3kW rating. Note that it will draw about the same 14 amps, but because it's 240v rather than 120v, the load will be twice the 1,650watts, so you'll get the full 3,300watts. That is all based on the charger capability and, as some have said, there were/are some software/apps limits, but I don't know if those have bene updated. Also, the above calculations are based on zero losses. There are efficiency losses with all chargers, so your output, in watts, to the bike will always be less than the watts consumed by the charger.
As others have said, using a 120v generator works fine and you simply set the Varg charge rate low enough to compensate for the sustained capacity of the generator. On 120v, even at max charge rate, it is fairly low (the 1,650watts estimated above). Like most generators, the Yamaha 2000 naming convention is misleading as that "2000" in the name is the max "start up" or "surge" wattage; not the max sustained load (or "rated load" or "running load"). The rated load on the Yamaha 2000 is only 1,600watts. You don't want to be right up on the max of rated load rating as it may trip when you are away or not paying attention and then an hour goes by with no charging. Set the charger to draw slightly lower than your generators 1,600watts load rating.
As for different voltages, amps and watts. V x A = W. So if you know two of those parameters, you can calculate the third. Since your generator can carry a sustained load of 1,600watts, that is 1,600 / 120v = 13.33amps. Set your Varg charger to pull 13.33amps or less (1,600watts or less) and charge away. It will be a slow charge, but slow is better than nothing. Not counting efficiency losses which are usually 5 to 10%, The Varg battery is 6.6kWh. If you set charge rate to about 1,500watts, it will take about 4.4 hours from 0% to 100%. If 10% losses, figure about 5 hours to charge. That means you'll see your battery gain about 20% charge per hour at 1,500watts input.