Ramble on Numbers as Identity

This one's really, really random, but it's just a thought I had. I have better rambles on the way, I promise.

In Logic class last semester, we learned how in ancient Greece, there was no concept of 0. If something didn't exist, why quantify it? Even 1 wasn't a number – it was a unit. The numbers started with 2, and they represented quantities. They quantified people or objects, such as a merchant's stock. That's why roman numerals were so easy. People weren't doing math with them; they were just recording that they had XXXIV of something, and the next day they only had XXVII left.

When did numbers start being used in ways that didn't quantify anything? When did they start representing places and people? We are all labeled by so many numbers, quietly nestled away in various systems based on these strings of digits that identify us. (And if they're just randomized strings of digits, can they even be called numbers?) Social Security numbers, student ID numbers, bank account and credit card numbers, College Board and AP numbers, even telephone numbers, street addresses, and zip codes all somehow identify us and where we're from. Yet they don't really quantify anything - they didn't start at 0. They're just impersonal and efficient ways to keep large quantities of people organized within systems.

So when, historically, did that happen? When did numbers stop being used just for quantities and start being used as labels?

That's my random thought for the day.