Nearly all societies of discrete individuals have developed systems by which those individuals can each be given a unique identify symbols, usually a name. However, the new category known as dividuals emerged during the Interplanetary Age, and their more complicated identities pushed the limits of the older naming schema to the breaking point and beyond. This spurred the creation of a standardized Dividual Naming Schema, part of the Dividual Interaction Protocols, to fullfil the same needs such dividuals had for unique identifiers.
The main uses for DNS are to allow dividuals to have informal referents for each other; and for dividuals to have formal designations with which to use to interact with a larger society. The method chosen to do so was based on a combination of peer-to-peer distributed software version control systems; an 'identity log', containing a record of the time and place of a dividual's significant life events; and cryptographic hashing, a mathematical technique involving functions which are easy to solve, but difficult to derive the inputs from the solution.
DNS is just one particular naming system, which that was developed early on alongside the Dividual Interaction Protocols, and as such, was the primary naming system used at the time, and had a certain influence in later naming systems. There have been several variants of the original DNS developed over the centuries, some of them complementing it, some of them openly competing with it. The Metasoft Version Control Identification Protocols of the Metasoft Version Tree, as well as the B.B.S. organometrics of the Carina Rush, are two notable examples.
The basic operation theory of DNS is that informal names should have the minimal amount of complexity necessary to distinguish any two beings in a given exchange. At the extreme, if there is only a single dividual involved in the interaction from a group with the label "DPR", then the minimal amount of differentiation they need to distinguish themself from another DPR is none at all, resulting in the informal name "DPR". If there are only two DPRs, then they only need a single bit of information, which in the DNS as written so far, is provided by giving one the identifier "1", and the other "2". Groups of dividuals who spring from separate 'ancestors' are presumed to already have different 'family names' - such as one set who call themselves DPR, and another set who call themselves "Keith Henson". The DNS is meant to be an add-on to whatever existing names are used that way.
For simplicity's sake, the identity log is a descendant of plaintext, in the form of an XML/HTML-type scheme. It is treated similarly to some present-day P2P file-transfer systems; it is divided into 'chunks' of standardized sizes, and a hash-value is generated for each chunk. When comparing identities, dividuals trade hashes back and forth, using variations of binary search algorithms, allowing them to quickly narrow down upon the point of divergence (while maintaining their privacy about the actual events).
Comparing the information of this entry - time, spatial coordinates, hash values, and a random seed in case of duplication - in both logs will have one entry with a lower set of numbers than the other; the dividual with that log would be "1", and the other would be "2". From this simplistic method can be derived a variety of further informal tags, such as the use of a name applying to all dividuals of a particular heritage, thus creating, eg, "DPR.1" and "DPR.2"; comparisons of further divergence of such dividuals, creating eg "DPR.1.1", "DPR.1.2", and "DPR.1.3"; and so on.
Should a set of dividuals be living in a society requiring every entity to have a unique identifier, then unless those dividuals deliberately limit the ways in which they allow themselves to diverge, the most reliable approach is to create an official register containing their identity logs, or at least those logs' cryptographic hashes, thus establishing an objective record which formalizes the informal naming schema.
This can easily get extremely complex extremely quickly, if the group of dividuals wants to do things that way. However, in most circumstances, it's probable that most of this complexity can be simply folded away and hidden from use - if there's only one DPR in the vicinity, e could just call emself "DPR", without going into any further specifics; and if there are only two, they only need the simplest comparison to have informal referents that are distinguishable from each other.
If all the tags of the identity log are identical, including the hash-signature generated from their current processing, and the random-seed generated during each one's restart, then their minds will, in fact, be identical - they'll simply be copies of the same mind running in parallel, and as such, generally won't need any name to differentiate themselves from each other.
If somebody edits the saved file of DPR.2.0, and starts a new dividual from the edit, letters are used rather than numbers, each different letter-set representing a different edit. So, the saved edited file made out of DPR.2.0 would be DPR.2a, and if a different edit was done, it would be DPR.2b, DPR.2c, DPR.2z, DPR.2aa, and so on. Instantiations started from such an edit would be DPR.2b.1, DPR.2b.2, and so on.
The single dot of the period in a name such as "DPR.1" elides a number of individual entries in the identity log. The double-dot of a colon elides even more. For example, if the dividuals who shared part of an identifier "42.7e.81" in their name achieve some degree of fame and popularity, then their various future instantiations may wish to include that sequence when identifying themselves, using a colon to elide extraneous parts, resulting in a name such as "DPR:42.7e.81:2.1".
Another factor that has to be accounted for is data loss over time - particularly when a dividual's identity log becomes corrupted. A question mark can be used to indicate such missing data, eg "DPR:?.1".
For merging various minds, brackets can be used to surround the differing sequences. For example, merging "DPR.2.1" and "DPR.2.2" could result in "DPR.2.(1)(2).1". If such mergings are not equal, then a vertical bar within the brackets can be used to give a space to indicate anything from simple weightings (such as a mind build from 20% of one mind and 80% of another) to more complicated creations, such as minds that are built on semi-independent subselves. Eg, "DPR.2.(20%|1)(80%|2).1" or "DPR.2.(N|1)(B,D,H,V|2).1".
DNS includes several optional protocols to allow for more aesthetic names. One such option involves the use of phonetic pronunciation, replacing punctuation marks such as the colon with onomatopoeiac sounds, which can result in changing "Dee Pee Arr point two colon six point seven" to "Dee Pee Arr pkh two pt pt six pkh seven".
Another option replaces numbers with words from a list, allowing for names which, while they can be decoded into numbers, do not necessarily sound numeric.