How you power tour fridge when traveling and boondocking really depends on the type of refrigerator it has.
If it’s a 2-way RV fridge where it works off of 120v or 12v+battery, then you need to have propane on and your batteries enabled for it to work.
If it’s a 12v only fridge, you need to just have your batteries enabled.
If it’s a 120v/residential fridge, you need an inverter installed and your batteries enabled.
While driving, your tow vehicle will send a trickle charge to the batteries they may or may not be sufficient to actually power the fridge and maybe slightly recharge your batteries. If you want a fuller charge while driving, look into installing a proper DC to DC charger.
For boondocking, you’ll need to recharge your batteries in some way. The cheapest method is just running your generator for some portion of the day. A more expensive, but quieter and less stinky method is to add a few solar panels- either in the roof or suitcase panels that you ground deploy.
You might find that depending on your fridge, age and size of batteries, and other electric use that your batteries die through the night. In that case, you’ll need to upgrade and potentially add additional batteries.