To give you an exact "latin" name would be next to impossible as there are many species of Brain Coral. This appears to me to be Lobophyllia Brain Coral.
Brain corals are actually colonial animals. They can create mounds 6 to 8 feet in diameter, in the wild (which looks extremely cool) and play an important role in reef construction. Endosymbiotic algae within its cells gives the coral its color. (This is a photosynthetic coral)
Collectively they are known as hermatypic corals (from the Greek god Hermes, speedy messenger). (just a stupid fact if your interested)
Care is straightfoward. It requires medium to strong lighting (as this is where is gets most of its "food" since as stated above it is a photosynthetic coral) however, you can feed them food like plankton, and brine shrimp. (brine shrimp are easy to hatch, and just about EVERYTHING in a reef tank can benefit from a dose of baby brine!
)
During the night they will put out "stingers" that can harm other corals if kept to close together. So try to space them away from other corals.
Water movement isnt really a big thing, however, medium waterflow would prolly be best. (I wouldnt blast em with a power head!) They do require calcium and strontium additives to be added to the water periodically, as they are a stony coral and use these elements in skeleton construction. Water parameters are no different than other other aquarium with stonies as far as salinity, nitrates, nitrite, phosphates and the like. Keep a clean system, and this is a pretty hardy coral.
Good Luck! (Nice local coral too!)
Jaybo