One could still be famous and still live in private. Take music producers for example, they make beats for artists and are popular among artists, but not so much the general public while still making more money than the actual performers.
So you could be a music producer. Hop into your lambo and on the way to your local Starbucks you won't be bothered when you walk out to grab your drink. On the other hand if you're a celebrity, you could be riding your bike around town and have a mob chasing after you.