Q:

Stumped: What would replace 'names' in an alternate history?

I have an alternate history epoch taking place in 10th Century Islamic Renaissance, but I have a large Bedouin tribe that does not use anything to indicate a person's name or identity.  This is a big Catch 22 every time I try to wrap my head about it.  
I don't want a number or symbol, I want it to be foreign for this tribe to refer to someone specifically.  Historically, they might say they are son or daughter of so-and-so (Bin So-and-so / Bint So-and-so), but I want to avoid any way to name a person.
In an effort to prevent this from being idea-generating or too-broad, and to be able to select a correct answer, I'll narrow it with the following:

Our 10th Century Arabic world;
People must be able to provide a response; if asked by the Caliphate "who did this," they cannot answer;
Numbers or symbols are not acceptable, as this would give identity.

In the end, I need a mechanism to make it impossible for someone in the tribe to name someone when questioned at length about 'whodunnit' even if they wanted to.  I think that this is impossible, so I'm bringing it to our WB brains.

A:

People would be referred to in a relative manner only.  So the person being questioned could refer to “my father”, “my second teacher”, “my kind neighbor” etc.  But a stranger could not go back to this town and use the same labels.  It would be “X's father”, but then who is X?  Without producing him, they cannot get a base for relative designations.  Without knowing the town’s people in some detail, such references don’t even make sense when used by people there.
These people would have to carefully use only designations that are relative to themselves.  Referring to something absolute, like “the mayor” (when there is only one) is a taboo.
There is still some intermediate ground though—the outsider might kill all the barbers because the target is “X’s barber”.

A:

So you want to do away with personal names? Seems like a daunting task. Names relate directly to a fundamental element of intelligence: identity. Humans aren't even unique in the animal kingdom in that they have names; dolphins have them too.
If you remove the capacity of a culture to be able to identify the perpetrator of an event, then you must strip away any concept of individualism within the society. There would be no 'me,' 'you,' or 'him.'
Instead of:

Michael planted the tree.
She painted the Hills of San Jose.

You would have:

The tree was planted.
The Hills of San Jose was painted.

This has interesting ramifications. If the society needs to identify, then it will identify as a collective:

We planted the tree.
We painted the Hills of San Jose.

There's no longer assignment of blame or accolades for a job well done. The Community succeeded. The Community failed. There is only The Borg Community.

A:

The answer is you.
If the tribe have no names, the only way they could refer to each other is direct communication: "You have food?", "You make fire", etc.
In this instance, everyone is you and no-one is individually identifiable.
Note that in this instance, it would be impossible for a member of the tribe to talk about someone else in the third person. That might limit their communication somewhat, but it gets you out of your whodunnit conundrum.

