The illustrators who genuinely achieve fame are few and far between. Even if your illustrations are recognizable across the globe, most people won't have a clue what your name is. You do get to have your drawings in print though, so at least you can point them out and brag that you created them.
There are those lucky oddities whose art places them on the same level of a Da Vinci, Picasso, or Walt Disney. Dr. Seuss, Beatrix Potter, H.R. Geiger, N.C. Wyeth—each of these are well-known names and have created immediately recognizable images and characters. Comic book fans will recognize Frank Miller and Brian Bolland.
Even grumpy Harvey Pekar had a movie made, which was about getting a movie made, that inner movie being about making a comic—a comic Harvey Pekar made about Harvey Pekar. The character even got an Oscar nomination.
Talk about art imitating life—a really strange, circular life.