Well, the "K" part comes from the fact that its discovery was published in a German science journal. Noting that vitamin K had been shown to be intimately involved with the normal coagulation cascade, the journal referred to it (in German) as "Koagulations-Vitamin", and the "K" stuck. Not that's it's any excuse, but that's the story.
Just why there are so many different B vitamins has a slightly more rational explanation. Initially, the substances collectively referred to as the vitamin B complex were thought to be a single compound. This was far from a careless oversight - chemical identification methods were constrained by the technology of the day, and all B vitamins do all share similar chemical characteristics (like their solubility in water), as well as often being found in the same sources. As successive, more advanced, tests were undertaken, it soon became apparent that there wasn't just one B vitamin. Furthermore, some of the compounds initially assumed to be part of the B vitamin complex were later discovered to not be vitamins at all, at least not in humans. Their removal left the gaps in the B vitamin numbers, but the remaining compounds have their scientific ancestory stamped onto their names with the letter "B".
The craziness of the vitamin's names is a case study in scientific inertia. Once something has a name attached to it, it is evidently quite hard to convince enough people to rename it, even if the new name makes much more sense.