In 1912 a Polish biochemist, Casimir Funk, published an article about food substances that could prevent diseases like beriberi and scurvy. Funk's analysis showed that these disease-preventing food substances might be members of a family of chemicals called amines. These substances were vital for a healthy diet, so Funk called them vital amines, or vitamines--spelled like vitamins, but with an "e" at the end.
That was 1912. By 1916 there was evidence that these disease-preventing food substances might not actually be what chemists call amines. The name vitamine was thrown out in favor of the names "fat-soluble A" and "water-soluble B." Only those two types were known at the time.
In 1920 another chemist wrote that the names "fat-soluble A" and "water-soluble B" were unwieldy. He suggested dropping the "e" from the old word "vitamine" and calling the substances vitamins. Whatever the substances might turn out to be, the name vitamin would be chemically permissible. As new types were discovered, they could be given letters--vitamin A, vitamin B, vitamin C, and so on.
Of course, this is just the history of the word, from vitamine to vitamin. The histories of the vitamins themselves are subjects for other Moments of Science.