We keep hearing that all the time to the extent that nobody really cares. Until something really happens and snaps you out of it. That sort of happened to me today. I just out of the blue Googled one of the accounts I use online (I'd rather not mention which one here for obvious reasons) and suddenly realized that, while I use that account to discuss pretty shamelessly about anything and everything, there were also results that linked that account to my real name.
The problem is that while you sign up with a user name, sometimes the website asks for the real name during the signing process. It wasn't a big deal before, but now that the websites have started to display the real names instead of the user name, skeletons in your closet are not so private anymore. Therefore the Photobucket account I made years ago, suddenly appeared on Google search when Googling my name. Going to that link you could find all my pictures that I thought nobody has access to, including photos of me when I was a dweeby little emo, my r-rated yaoi drawings and it all accompanied with my full name and a passport photo.
This was next to my complete name in Photobucket
I was so embarrassed, I first deleted my name from the account, then deleted each picture one by one and finally deleted the account for good. As if that would delete them a little better. I wish there were a "delete this content from the cyber space forever" button, but there isn't. The pictures cannot be found from Photobucket anymore, but they're probably still somewhere, somehow.
If you wanna stay "private" online, you gotta be more careful theses days; keep your real name and user names strictly separate. Actually these days when websites ask for names, I give a fake name that is derived from the user name. And think hard before posting anything of you online. I posted a video of me that I can't delete since I don't have an access to that website anymore cause the logging in was from a third party website from which I deleted an account. Internet is really a crazy web. I hate that it's there, but I can only wish that my emails to the admin may reach one day.
I don't think I even realize how far the Internet surveillance has advanced in the previous years. It's not that unlikely for your future boss to check out your google searches.