I don't know of too many common names out there for describing the brains. I usually hear a descriptive terms with a loosely put brain type such as neon green mounding platygyra worm brain or red rimmed encrusting pentagona war brain. Then there are favia varieties that start to connect valley\mouths and get the slight appearance of a brain ,especially once they have attained a larger size, Grape favia comes to mind, these can be commonly called closed brains as well. Another example of why there are the scientific latin names we all try so hard to learn, I try and find a happy medium by knowing both to the best of my knowledge...maybe one day we could have a form of ID page.