It’s alway better to tell the mechanic what to fox rather than tell him what to do to fix it. Had you asked to have the problem diagnosed rather than just to replace the alternator, you probably would have saved yourself the cost of an alternator.
Since you’ve already had the alternator replaced, I’m betting on the battery. Have the entire charging system and battery tested and all teh connections checked.
I’ll bet my morning muffin that the battery is original. Do I owe you a muffin?