I cannot find anywhere how to say vegan in russian, only vegetarian.
веган or (rarely)
веганец in Russian, the word is a typical internationalism. The word for "veganism" is
веганство (analogous to "вегетарианство") or just
веганизм. This word has appeared pretty recently in Russian, so no major dictionary has it (some of the newest ones do have it), but in the Russian Wiki there is an article about it.