It was made up by Donald Watson, who founded the first organization for those seeking a lifestyle free from animal products in 1944 in London. Watson and his friends – correctly – thought that ‘non-dairy vegetarians’ was a bit too long a term. So they agreed to create a new word, something shorter and easier to say.
Many options were considered, including vitans, dairybans, benevores, and allvegans. They eventually decided on “vegan” as it took the beginning and the end of the word “vegetarian.” It may also have been influenced by the fact that a popular London vegetarian restaurant was named “Vega.”