if you don't want anything, then why any replacement? And what do you understand by replacement if you are not going to actually replace them? Common meaning of replacement is something with the same functionality, isn't it?

@Mołot I'd like it to be nearly impossible for someone to be able to pinpoint an exact person when interrogated, even if they wanted to, given the time, geography, and sociological context of the story. I, too, am at a loss.

As one of the answers points out: this concept goes SO completely against the fundamentals of human nature as to make the "alternate history" aspect of the story lose credibility (to me). You might as well write an alternate history story where ancient Rome is magically transported to Mars. Fundamental human psychology DEMANDS unique personal identifiers. No society in history has EVER gotten rid of them.

You may be overthinking it. Find out "who did this" is useful in only two situations: to find out who is responsible for something bad, or for somebody to boast that they did something good. Up to relatively recent times there was no judiciary police; in many places, the state/caliph/lord did not care specifically who did something bad, but only where it happened: the nearest village would then have to pay the tariff (so much for cutting a tree, so much for murder) and it was their problem to find out who exactly was the culprit.

Please take a look at the answers to this question: worldbuilding.stackexchange.com/questions/62648/… which can give you a start--although you seem stricter about it. My answer actually references cultures which come close to this and why, but it certainly is not as strict as this.

In such a society, if "whodunnit" is unanswerable, the legal system will have difficulties: Nobody could be tried and punished, not debts could be collected. Hence all trades would have to be immediate (probably not even money could evolve) and misbehaviour could only be penalized by some sort of immediate revenge.

The whodunnit could still be solved by the time-honoured practice of gathering everyone together in the parlour. Instruct one of the tribe members, "Point to the person who dunnit."

@ErinThursby - this is a very good start; I don't know why I never saw this original q/a

@JBiggs - This is not entirely against 'human nature,' I have traveled with Bedouin in Tunisia and Algeria and nomadic in Mongolia. It might be against 'Western' or 'Modern' nature, but not 'human.'

I don't understand the point "People must be able to provide a response; if asked by the Caliphate "who did this," they cannot answer;" The first and second parts seem to be in contradiction. -- The Caliphate asks "who did this", and then what do you want to happen? Are the tribes people at a loss for a response? Do the respond with an identifier that makes sense to themselves but not to anyone else? -- Basically, are you looking for a concept of a label that is not "a name" (that is, doesn't identify a person), or are you entirely against the concept of labels (even non-specific ones)?

@GreenstoneWalker or just gather the entire tribe suspected and start killing people until someone comes forwards and admits...

There are cultures that do not employ [personal names]( en.wikipedia.org/wiki/Personal_name). The Wikipedia article mentiones for instance the Machiguenga of the Amazon.

@Mikey, I spent 10 years living in the Middle East. Bedoin ABSOLUTELY DO have unique personal identifier names! Not only that, but while there may be unique customs or patterns of naming among various cultures, there is not a single culture that doesn't (or didn't) have ANY way to identify a member of the group. Even animals do that. It boils down to human consciousness.

What would replace 'names' in an alternate history? Guids

@JBiggs - Yes I lived in the Tunisia and Abu Dhabi, both urban and Bedouin. This is an alternate history where one of the tribes cannot tell the Caliph who committed the crime, because in this alternate history, there's not a way to name a person in the tribe.

Use the Roman system, name everyone the same damn name. Scipio son of Scipio, son of Scipio. Scipio went on to become nicknamed Scipio Africanus, not to be confused with his grandfather Scipio Africanus... So yes they have names, but that does not actually help much.

The solution, obviously, is to use the same Marklark for every Marklark!

Would something like the aboriginal system help, with some adaptations? Everybody used to be brother, sister, aunt, uncle etc.. in day to day speech when I lived in Australia. en.wikipedia.org/wiki/Australian_Aboriginal_kinship

Do you want to do away with the very notion of them being able to identify individuals, e.g. "We are Borg" or "We are all part of the Great Link" to use Star Trek-isms? You first need to define the mindset of the tribe members when dealing with others. If they have a way of identify individuals then that's really just names again. If not, then how do they see others? e.g. as a single collective group? Is it "me and them" or "all of us"?

You could use a combo of description and skill. Description as in the old native Indian way: fast-foot, pale-face, etc. Skill as in the exact skill of that person: carpenter, hunter, etc. That way you can get to something like fast-foot the hunter, pale-face the carpenter.

Maybe tribal markings like "Face scar" or maybe identify each other by numbers... though I guess that could be considered a name.

Does a single, large Bedouin count as a "large Bedouin tribe? All the members of the tribe would be large. That's the only way I see this working.

If this has to be a one time occurrence you could just pull an old classic, the person's name is "Nobody", so when asked who did it everyone replies "Nobody". just make the asker not clever enough to figure it out. Works even better if they speak a different language than the caliphate, and "nobody" does not mean nobody in the local language.