Under which name is this fish known?

You can't put two males together as they'll fight. A solitary male has also been known to fight its own reflection on the glass of an aquarium.

Betta looks like the Peacock Fish/Underwater Peacock

You are so Right Red sea Diver. I was wondering why my two males are always so Irratic esp. my Platinum betta. they act all Irratic not really my dark blue one anymore hes just lazy. but my female betta is so cute very smart not at all Irratic.

Just the Males, but a female & a male will also if the tank is to small. if you put 2 males in a really big tank together they will not Kill eachother. I have 2 males 1 female betta they are all together in a huge tank. it's been a Year now.

We returned from vacation to see our house sitter had bought a red fighting fish for us. Looks almost exactly like the photo.