Well, the giant white one is a white platinum ogon. The white orange one is a Doitsu kohaku. The long brown one looks more like male green which is called a Midori (also called Midorigoi). If it's a real brown one (for light can change the color), it's a Chagoi. The socalled black one is a bit unclear for the water doesn't make it clear to me wether this is total black koi or a partial black one. Which makes it a possible Karasu, black ghost, Shiro utsuri or a Kumonryo (also known as dragon koi). I do think that the two first mentioned options are most likely in this case. I've kept and bred koi fish ever since the mid 1980's up till 2005. In fact for every color variations you can put the name "goi" behind it. It's the Japanese spelling for "koi". Spelled like "koi" is also japanese but a western spelling.
If you have a number of koi in your pond and you want them get tamed in a short time, it would be a good plan to get a Chagoi, a MIdori, Soragoi or an Ochiba shigure. These color variations are the most tame ones. And if you'll put one of them in a group, the rest will copy its behavior.
