The names are going to be the color and type as the name, unless you got them from an authorized dealer that you can stamp whatever color name they made up to call it. If you go on ebay or google and type in the color and type that you have, you might find a best match to call them.
Green Rhodactis
Red Discosoma
Orange Ricordia
Etc, etc..
Corallimorpharia corals are typically called mushroom corals. Some hobbyists also call them disc anemones, false corals, elephant ear corals, umbrella corals, and mushroom false corals.