Are you asking for a recommendation for 12V inverter that can run that well pump? Sorry, I'm not clearly seeing why you have 4000W DC in the thread title.
Well pumps are one of hardest loads that inverters face, especially 12V inverters. Sometimes it can make more sense to replace the pump with something like a Grundfos SQ than buy a big enough inverter to START your current pump.
Are you able to measure the starting amperage of your current pump?
Most folks are going to steer you away from a 12V system if possible but there's probably more going on.
I'm guessing you're trying to have a backup power source for your water that can run off of one 12V battery?