Would not the opposite be true? If you have to write your name out just so the mail can find you, you are less anonymous than if you just have a number that gets mail directly to your mailbox.

You divulge your name yes but the upside is not having it correlated with a place. The name is written on the mailbox outside but is not mapped to a unit number on the envelope/parcel nor on the building.

The only way anyone can map your unit to your name is by physically watching you collect the mail then return to your unit.