Going to make an assumption that you have a residential fridge.
Make sure your house and aux battery switches are turned on. Make sure the cutoff switch in the bay where your inverter is located is turned to the working position (if you have a switch) Lastly, make sure your inverter is on.
Your engine charges your house batteries as you drive, Your house batteries run the inverter. The inverter runs the fridge.
Before your trip make sure that your house batteries (possibly located under the entry steps) are filled with distilled water, and charged. This would be the reason to run your generator if you are not plugged into shore power.
The other reason to run your generator on a trip is to be able to run your coaches AC unit(s) as you drive.
Congrats on your new RV!