What can you name a cactus?

It's an easy choice to name a cactus after its common name. But there can be confusion and overlaps in common names. So a more precise, unique choice is opting for a cactus' scientific name. So for example, a prickly pear cactus can be called Opuntia; or an old man cactus Cephalocereus, Espostoa or Oreocereus.