Good. Tell me how many business owners you really know who are clearing 1M+ a year for themselves other than a few on the internet that show off ? The answer is: not many or hardly any. So you are overthinking the fame part. You won't be as famous as you think you will be just because you run a successful business (Source: I run a reasonably successful business and I am a nobody)

So the question really is: What is your motivation behind remaining anonymous ?