Common names of anything - 'designer' or otherwise, vary.
The only constant is going to be the scientific name, assuming it's correctly identified. Not so much with Zoanthids, but with some corals, even the proper scientific ID can be tricky.
But the designer name for those is "radioactive dragons eyes". Nice ones, too.
Mine like light & medium- high flow. Look around and you'll see the different adaptations/ morphs it'll go through depending on conditions in your tank.