tl;dr. No. Implementing a system of absolute identification across the entire Internet 1) would destroy the inherently distributed nature of the network and 2) is probably completely impossible anyways.
In it's most basic sense, the Internet allows any computer (and by extension any person) to communicate with any other computer/person on the network. Every client is (or at least should be) treated equally. It's what makes the Internet powerful and what makes it dangerous. It's led to drastic changes in all of our lives.
I can connect with more than a billion people on Facebook… I can find something about anything on Google… I can listen to any song ever on Spotify…
I have super powers.