Fame
Karl Pearson. R.A. Fisher. Jacob Cohen. Gertrude Cox. Kirstine Smith. Do any of these names sound familiar? No? Then perhaps you've got an answer to the question of fame and the statistician right here.
Then again, here's one name you just may recognize: Florence Nightingale. Although she was remembered as a pioneer of nursing and hospital sanitation processes, when she was recruited as a nurse during the Crimean War, she collected data and systematized record-keeping practices. Karl Pearson, the first guy you didn't know up there, eventually acknowledged Nightingale as a "prophetess" in the development of applied statistics.
So yes, there is a famous statistician, but then again, it's not really what she's famous for.