Some illustrators achieve fame, but not many. Even if your illustrations are recognizable, your name probably won't be. You do get to have your drawings in print though, so you can point them out to everyone you meet and brag that you did them. If you're the braggadocious type.
Dr. Seuss, Beatrix Potter, N.C. Wyeth—each of these are well-known names and have created immediately recognizable images and characters. But where are they now? That’s right - dead. So you see where fame gets you.