I'm not a big fan of fame for fame's sake. Fame is vastly overrated if you ask me – and if you don't want to ask me, spend ten minutes online searching for celebrity meltdowns, famous scandals, and the like. You'll quickly realize fame really is kind of overrated, and is too often transformed into infamy.
On the other hand, fame is a very useful tool – if you pursue it with the intent of actually using it. Being known gets you jobs, gets you contracts, gets you roles, and so on. Fame as a tool, where you are it's master not the other way around is quite useful.
So frankly, you're going to have to confront the issue of fame in your life and career – can you use it, how do you want to use it, how do you get the right kind, etc.