Actually the “ASE” prefix came from “Allegro Sprite Editor,” the old name of Aseprite. Then I renamed to an easily googleable term (a word with 0 results on Google), and aseprite.org domain was available, so “Aseprite” was a great candidate for the new name of the program (+ keeping the old name as a prefix).
P.S. Allegro was a game development library used to program ASE from the very beginning (this year Allegro was finally removed from the Linux port, and now we use our own code to handle windows and mouse/keyboard input).