There are two things about this that don't require centralized identity.
The first is that it's very commonly not true at all. If you want to sign up for an account for an online service (e.g. email, YouTube, gaming), they don't need the name on your driver's license for anything. They don't need to know anything about you. You create an account, set up authentication to prove you're the account holder in the future, and that's it. The identity you use can be created along with the account; it doesn't have to exist beforehand or be associated with anything else.
Second, even where reputation is important, you still don't need a single identity, it's just that an identity without any history would be untrusted.
Suppose you go to the bank to take out a loan. If you tell them your name is Barrin92 and you have no financial history, they're not going to give you one unless you get some more trusted party to cosign it or you post enough collateral that they can be assured to recover their principal if you default.
But then you start off with a small loan with a large amount of collateral, or a cosigner, and build a credit history as "Barrin92" with financial institutions. Now you can get a bigger loan, or one without a cosigner or as much collateral. Until you default. Then "Barrin92" would no longer be creditworthy and you'd be back to square one.
This works fine even if you have a thousand separate identities, because identities with no credit or bad credit aren't trusted and good credit is valuable so that you lose something significant (the creditworthiness of that identity) if you default.
People having multiple identities is effectively just equivalent to the ability to declare bankruptcy. It doesn't really break any good important thing and it does break some important mechanisms of oppression that we should want to break.