That's a Stiphodon, likely a male S. atropurpureus in breeding colours. There are lots of species, many very difficult to identify. In any case, maintenance is all pretty similar: These are hillstream fish that need relatively cool, well oxygenated water. Water chemistry not critical, though while spawning occurs in freshwater the larvae appear to develop in the sea. Diet consists of algae and aufwuchs in the wild; in the aquarium they are variably easy to maintain on algae wafers, squashed tinned peas, finely chopped prawns, bloodworms, etc. Some species seem to do better on such foods than others; provisionally at least don't combine them with more active feeders until you're happy your gobies are feeding well.
Cheers, Neale