I know is very difficult to have such recognition when you are working for a company and you are being paid to give up your name and put the company first. Although I have to say that the most successful companies help their employees to be recognizable, and this is because the company also benefits from it. Remember the long story of Steve Jobs? Such genius couldn’t be hidden for long. If you have the blessing of working for this kind of company that allows you to use your name, then do it. What do you think?.
I think it is a common understanding now that you have a person brand whether it's public or not. Your brand is your character and skills as seen through your behaviors and your professional image.
I think the point of your question, though, is whether or not you can promote your personal brand (using your name) outside of the company that writes your paycheck. I see no reason why not as long as it does not diminish the brand of the company paying you.
I ran my own consulting company for 15 years and building brand recognition was difficult. What I really leveraged to get clients was not a logo and catch-phrase but my personal reputation. I could easily have named my company Michael Wilkes, Inc. or some such and dispensed with the whole company name brand building effort. My attorney, of course, would probably disagree sharply based on the value of a corporate liability shield.
The introduction to the book "Brand You" contains this sage advice:
'You already have a brand. As Jeff Bezos, the founder of Amazon, once said, “Your brand is what people say about you when you are not in the room”. The best way to market yourself is to build your brand.'