I could be wrong about the name; someday maybe it will flower and I can get a better idea. It likes full sun and medium water during the growing season. The cuttings root easily.
All of my 'Corryocactus' were taken from a single small crest that just keeps growing. Maybe it's an Opuntia?
The uncrested form makes long curvy stems that look good in a hanging basket. You'll want lots of headroom. Hanging it at eye level is just asking for trouble.
It's a very easy plant to keep alive and no two look exactly alike.