The fan draws a lot of amps. Add in headlights, other loads, you may be just exceeding the output of your alternator.
Stock size is not always big enough.
The only way to tell for sure would be to know the wattage rating of the alternator and measure it under a load.
But if its a fairly large one, then check the usual suspects.
Bad ground on the alternator. Some people run a heavy cable from the frame of the alt to the ground wire hookup point.
Bad connection or too small wire coming out of the alternator.
If yours has a separate voltage regulator, it may be bad.
Plus, the one that used to be the most likely one, loose, glazed, or slipping belt.
Modern serpentine belts have mostly eliminated this one. I used to check it by running the car with everything electrical turned on for a couple of minutes.
Turn the car off, and Carefully touch the alternator pulley.
If the belt is slipping its going to be really hot.