My first thought is what is his water temperature? Air temp and water temp often differ even in climate controlled rooms. The water is usually a little cooler because it takes more energy to raise the temp of air than of water. Bettas in cool water don't like to eat. They should be in temperatures between 76F and 82F.
Betta can easily be kept in 1 gal tanks, but you should be changing the water twice weekly. When was the last time his tank was cleaned?
If his water is clean and warm, then all I can tell you is he is still adjusting. I've heard of bettas taking a little longer than 2 week to adjust. They can go a long time without eating. Just keep trying to feed him and remove any uneaten food.
Oh and welcome to the forum!