As far as I am aware, the oldest name we have written down in an archaeological context is that of Iry-Hor, a predynastic king of Upper Egypt who reigned during the 32nd century BCE. You can see what I understand is the earliest inscription bearing his name here, which was found in the Sinai in 2012. We know of a couple kings who are supposed to have preceded him, but as they are proto-writing, we only know them by symbols, such as Scorpion I and Double Falcon and Bull, not their actual names, just our names for them.

We have some other names on Mesopotamian inscriptions from the Jemdet Nasr period, which is from the 31st century to the 29th century BCE, so later than Iry-Hor.

Edit: the latest scholarship on the topic, and the publication of the 2012 inscription is in French, and can be accessed online here.

If their name must refer to a spoken sound by which acquaintances would have referred to a person, then the oldest we have currently are a slave owner Gal-sal and two of Gal-sal's slaves Sekkulgir and Enpap-x who lived in Sumeria around 3200BC. I don't believe we have any information that sheds any light as to which of the three is the eldest.

There are older symbols from China that could be names after a fashion. The oldest I'm aware of are from Jiahu around 6600BC. They are not believed to be actual writing but rather a precursor. The meaning of the symbols is largely speculative, but one hypothesis is that they indicate ownership, like a cattle brand. If they indicate individual ownership then they refer uniquely to individuals and are therefore effectively names.

And of course it's possible that we'll uncover names older than these. In so doing we become aware of them and so the person named must not have experienced the second death to which you refer. Pretty sure I heard that same story on NPR, by the way.

I believe that this quote originally came from Irvin D. Yalom, and it refers to the memory of a person, not just knowing their name. For instance, we know Abraham Lincoln's name, but no one who knew him is still alive, therefore he has "died" for the second time. You may be referring to another, third death, when humanity forgets.

"Some day soon, perhaps in forty years, there will be no one alive who has ever known me. That's when I will be truly dead - when I exist in no one's memory. I thought a lot about how someone very old is the last living individual to have known some person or cluster of people. When that person dies, the whole cluster dies,too, vanishes from the living memory. I wonder who that person will be for me. Whose death will make me truly dead?” ― Irvin D. Yalom, Love's Executioner and Other Tales of Psychotherapy

As a related question, who is the oldest woman we know the name of? It seems like everyone mentioned so far is a man.

Some time back I wrote an answer to this question looking at the oldest human name that we know, and I took a linguistic approach that is a bit different. Here's the link and here's my statements on it. I'll add that many cultures have founding heroes that go a long ways back, for example Dene creation myths seem to fairly clearly go back to the Pleistocene, implying that we have a person or people who yet live in memory despite having undergone the first death when megafauna still roamed

Oldest as determined by date of record? By date of legible record? or by date of reconstruction? There are a few ways to approach this question from a linguistic perspective that are likely to give you names that we can determine reliably, but a few things first.

almost all names in the world are derived from descriptive phrases. The stereotypical Native American "running wolf" style name, is actually more indicative of how names generally are created than is the idea that we have names like "John" or "Mary" that have no immediate meaning.

Secondly, names that have no immediate meaning, are generally developed from previous names that did have meaning. Most of our names today come from either Semitic names (with definite meanings, via Christianity) or from previous descriptive phrases in our own languages that had meaning, or from even earlier. For some examples, here's a little description of proto-indo-european names with examples (link).

Now if you are looking for the earliest names we can recover, the place to look is in reconstructed proto-languages, for example try this list of Proto-Indo-European Deities. In it we have names like *Dyēus Ph2tēr which has come down as Zeus, Dios. this was a name back some time between 3700BC and, some have argued, maybe as far as 7 or 8 thousand BC. the thing is, this is only one proto-language, and there are many others, some of which are likely to be older such as niger-congo languages, and so on. All of these language families have naming conventions that can be traced across them, allowing us to trace back likely names that would have belonged to individuals many thousands of years before recorded history began.

Now as to recorded names, there's one final thing I'd like to throw out there. Many many cultures have multiple names for individuals, for example they'll name people after things they have done. This means that likely some of the oldest rock paintings in the world, such as the Bhimbetka rock paintings in India could very likely represent recorded human names along the likes of "killed a buffalo" or something similar - a name that might be 30,000 years old. Though phonological data might not be recorded, it still might fit the definition of "recorded name".

Now for the last step, and going back to linguistics again. And this is the most controversial by far - there are several linguists who support the idea of what is called Proto-Human or Proto-Sapien language - the proposed most recent common ancestor of all human language. On some levels, this isn't that extreme - we know that the alphabet has only been invented once, and all other alphabets have been by borrowing, so why not language? That said, this is a highly controversial, and generally discounted idea, though of course still innately appealing. For example, Merritt Ruhlen gives a list of proposed proto-human words, at least one of which could have been a name at one point - boko (arm). In addition, he includes a word that could have easily enough been a name, nickname, or putdown - putV = 'vulva'.

I suspect if someone were to do a deliberate search for the oldest recoverable name, it would be possibly to come up with a very likely name that could be reliably traced back to at least six or seven thousand years before present.

Why is this thread title orange?