Can anyone tell me what the name of this succulent is? Looking for better care advice for it and think knowing what it is will help

It might be Portulacaria afra which is elephant bush.

The glass pot is not a good idea unless it has drainage holes. It needs a cactus type soil, fast draining and quick drying. Perhaps a mixture of 2/3 cactus soil and 1/3 potting soil might work for you.
Elephant bush needs as much direct sun as you can give it, 4-6 hours a day for optimum growth.

I agree with BigBill on everything except the soil -- use cactus soil only, and if all you can find is an inexpensive bagged mix from a big box store, add extra perlite to it as well.

I also agree, Elephant Bush (Portulacaria afra)