I believe a lot depends on what your name is. If you happen to have a common name or the same name as a well known person it may be virtually impossible to establish your unique identity on the internet using your real name. For example if your name happens to be Bill Gates you could not live long enough to be THE Bill Gates on the internet. By the same token if you happen to have the same name as a notorious person like Bernie Madoff or Moammar Gadhafi your task will be extremely difficult.
What you really want it to be known by an easy to remember, easy to spell and favorable moniker. This is why so many actors and performers take on stage names.
In your particular case, Hartley Brody, you have a great name and there is no reason not to use it. You are already well established in Google so you are doing a good job.
For others, particularly someone whose name can't be represented in the roman alphabet trying to sell products and services to English speaking customers, a moniker may be the best option.
In my case I use the handle JonnyBoats, but I do not hide my real name, John Tarbox. (easy to find in Google). I do believe it is important for people to be able to know who you really are if you expect them to do business with you.
If you think of the computer industry there are lots of people who use handles and are well known by them, ScottGu at Microsoft for example.
EDIT: My apologies Nikolas Nikolaides, you have a fine name as well. Unfortunately when one Googles your name the response is:
Did you mean: Nikolas Nikolaidis
which means you need to do more work if you wish to establish your name as a well known brand. Also there are two (2) Nikolas Nikolaides in LinkedIn, which further contributes to brand dilution. In your case I guess a lot depends on if you can get the user name Nikolas Nikolaides on all the sites you visit or if the other Nikolas Nikolaides has gotten there ahead of you.