TPF is mostly freely accessible for anyone to browse and read, which also means that search engines (like Google) have the ability to read and index its contents.
As with every interaction online, it is important to realize this and remember to only post contents that you are comfortable sharing with complete strangers. The amount of your privacy is determined by the things you post or do not post.
Keep in mind: A search for a globally unique, seemingly random username will certainly bring up someone's TPF posts. But a. why would anyone search this and b. they could find the same (or even more accurate search results) via the TPF search if there was really the interest in your postings.
We can not and will not make all of TPF private, we may offer some more private sections at some point in time perhaps, but there is no plans for this right now.