The second question in the '36 questions to intimacy' project:
2. Would you like to be famous? In what way?
Only a media outfit would think of that: fame is their bread and butter. I don't think that a mature adult would even think about 'fame'. To do so would be narcisistic, and it misunderstands 'fame'. People are not just famous. Their fame is an outcome; usually of achievement.
I'd imagine that people see fame for currency: it is productive of either wealth or power (or adulation for the narcissist). Maybe some people would be famous for doing 'good'. Mother Theresa springs to mind, but few. On the other hand, Tim Flannery is famous for getting it wrong...again and again. Do you want that?
My answer is 'no'. The second question then falls away.
But if the question is 'what would you like to be known for' that's different.
I avoid any temptation to go off into fantasy land (thus, I wouldn't want to be known for being a great...anything): instead, I would want to be known for loyalty, love, and being there when needed.