Hi Terri,
It's an Adenium and they are called the Desert Rose. If it were mine I'd remove it from the pot to check the roots to see if they are rotted. Then I'd repot it in a fresh well draining mix. I use cactus mix with 50% more perlite or pumice added. Keep your pot wide, but not deep.
They love to go outside. First put them in shade and gradually move them to full sun. They will leaf out and bloom well in full sun. When it's winter you can let it go dormant, and put it in inside or in a garage with very little water. In summer it can use a lot of water. Many of us have to water ours daily. Watch for insects. Mine are prone to mealy bugs.
I think many people treat them as a cactus, but they like to be treated as a tropical, water loving plant.
