Is that why you're doing this? Are you avoiding all of the advice of your parents, teachers, guidance counselors, and others that you should get a "real" job in order to pursue worldwide name recognition? Well, that's probably the worst reason to become an actor. Sure, it happens, and when it happens it's absolutely delightful. But for 99.9999999% of actors out there, it isn't going to happen.
You may experience some fame to a lesser extent among your peers, whose respect and admiration may make you feel very good inside. And maybe you luck into a national laundry detergent commercial that makes all your high school classmates think that you're a superstar. But you'd probably have that same level of fame if you were a really well-respected cardiologist instead.
Even if you get a massive amount of success as an actor, you may still not end up being famous. Do you know who William H. Macy, William Hurt, Paul Giamatti, Joan Allen, and countless other award-winning thespians are? Well you might, because you're into this business, but nine out of ten people won't recognize the names, and even if you show them a picture they'll just go, "Oh that's the person who was in that movie I really like." And it's even worse for theater actors, whose fame usually doesn't leave the boundaries of New York City.
On the opposite end of the spectrum, Mark Hamill had like one big role in movies (Luke Sky...something) and since then has lived the simpler life of a voice-over actor―but thanks to that one role, even people in far-flung places like Uzbekistan, Fiji, and Montana know who he is.