She is one of a gajillions of Borg drones. What exactly does "Seven of Nine" means as far as drone identifications? Shouldn't she have some GUID instead?
You're assuming there is a unique identifier for Borg drones. They could very well just have "disposable" identifiers assigned to them when they are awakened to join a group and perform a specific task.
Also, Iirc, there's a Voyager episode where Seven needs to coach a human team and she assigns them numbers. When one of them "fails", she just re-numbers them so that 4 becomes 3 (and takes over with the task), 6 becomes 4 and so on. That suggests that Borg consider their "names" as something that is subject to change and can efficiently handle that. She used those numbers as roles identifiers more than as GUIDs.
If there's GUID for Borgs (DNA signature? Assimilation serial number?), it would be pretty inefficient to state it completely in communications.
(Note, btw, the similarity with the soldier identification scheme in the Roman Army, where soldiers would decline their legion, cohort, century, etc. numbers of the unit they belong to)
The # of # designations are, as others have pointed out, rank of total on a ship/station and then jumps way out to subdivision of region(unimatrix). This is not sufficient to uniquely identify an individual.
Let's get speculative, seeing as the canonical answers aren't satisfactory here. When do Borg use these identifiers? In verbal communications. When do Borg communicate verbally? When they are speaking to other species.
The Borg designations are only used in the rare event that verbal communication is needed. In interborg communication there is no identity, and this undoubtedly involves more computer-like unique ids and networking. Probably mesh networks over subspace and transwarp conduits.
TL;DR: What we are mistaking to be "names" of Borg, are actually "designations". There's a distinct difference in that a "designation" is more like a rank or job title, whereas a "name" - as humans understand them - is a persistent, unique identifier of an individual.
A single Borg may have several different designations throughout its lifetime, and it is possible that a single designation may change hands between several Borg. Further, when the designation is simplified to "X of Y" without any of the additional qualifiers which are a part of the full designation, it is very probable that many Borg exist with the same shortened designation.
We may not know for sure whether the Borg actually have persistent, unique identifiers like we have names - it does not seem to be addressed in canon. However, it would be hard to imagine such a complex Collective being able to operate efficiently without such identifiers.
I think @sylvianulg got closest to the truth, though I'm still not sure the analogy (used by some others) of a router assigning IP addresses is quite accurate.
First, let's go over some facts (see links and quotes below for reference):
Seven of Nine's full designation was Seven of Nine, Tertiary Adjunct of Unimatrix 01.
Unimatrix 01 is known to currently have nine drones, each designated [One-Nine] of Nine, with some having an additional functional designation such as Primary Adjunct or Auxiliary Processor
Formerly, Unimatrix 01 had only five members, with primary designations being [One-Five] of Five.
A Borg drone's designation represents their position within their Unimatrix or Trimatrix.
So, the designation a Borg gives to outsiders is more of a rank or title - and, when they give only their "short name", it's a fairly non-specific one at that. For example, "Seven of Nine" could refer to the Seven we know or it could also refer to (if one existed) "Seven of Nine, Auxiliary Processor of Unimatrix 42".
That said, it is also possible that Seven previously had a different designation. Perhaps one might have been "Four of Eight, Secondary Adjunct of Trimatrix 626" before she was re-assigned to Unimatrix 01.
What is important to realize here is that Borg "designations" are not "names" in the sense that humans understand. To us, names are (generally) unique identifiers of an individual. The Borg designations are an identification of the individual's position or function.
The unique identifiers - the true "name" - of each Borg will probably never be known outside of the Collective. However, I believe we can be fairly certain that such an identifier does exist. Proper resource tracking and allocation can not be achieved without being able to uniquely identify each resource. It is probably some sort of long GUID which is assigned to each Borg when it is first attached to the Collective. Since such complex identifiers would be impractical to use when communicating with species outside of the Collective, the Borg instead chose to fall back to their designations when such communication is necessary.
To bring this into a networking analogy, the operation of routers & IP Addresses comes close but is still not quite correct. Let's consider instead hostnames and asset tags, used to identify and track servers in an organization.
When a computer is first purchased, businesses will generally put an asset tag on the system to track it for inventory purposes. That asset tag is usually kept on the system, with a unique number and/or barcode, throughout its life - from its arrival in Receiving (before it is even put into use) until it is permanently decommissioned (destroyed, or transferred outside of the organization's control). The asset tag here represents a (relatively) life-long, unique identifier that will not be shared or re-used on any other resource.
Hostnames, on the other hand, are often used to identify a system's function. For example, MySQLSRV-05-03 might be node three in SQL cluster number 5. These names might be shuffled around and re-used across different unique systems, because they relate more to the systems' function than they do to its identity.
Example: A new system is purchased to act as a VM host. On arrival, it is given Asset Tag #01701. Once installed in its role, it is given the Hostname VMH-09-07 because it will be the seventh VM host in group number 9. Some years down the road though, the system is beginning to show its age - it just doesn't perform as well as the newer models, and can no longer adequately serve the business' needs as a VM host. However, it is still quite well suited to be a file server. So, a new server is brought in to replace it. The new server, Asset Tag #74656, takes on the Hostname of VMH-09-07 when #01701 is taken offline for reconfiguration. The old VMH server still retains its identity as #01701, but when it steps into its new role its Hostname becomes FS-12-04.
Below are quotes from Memory Alpha, which serve as the primary basis for my analysis:
Drones within a unimatrix or trimatrix are designated in groups known as "adjuncts", with the individual drone's identification serving to designate their position within the adjunct. (VOY: "Dark Frontier", "Unimatrix Zero", "Endgame")
Seven of Nine (full Borg designation: Seven of Nine, Tertiary Adjunct of Unimatrix 01)
Known drones assigned to Unimatrix 01
One of Nine Two of Nine (Primary Adjunct) Three of Nine (Auxiliary Processor) Four of Nine (Secondary Adjunct) Five of Nine Six of Nine Seven of Nine (Tertiary Adjunct) Eight of Nine Nine of Nine
Previous drones assigned to Unimatrix 01
One of Five Two of Five Three of Five (Tertiary Adjunct) Four of Five Five of Five
Seven of Nine was Seven's designation within the Borg collective. As an assimilated individual has no need for a name within the collective they are given a number relative to their function within the collective. Generally a Borg will refer to itself by just its number; Seven (of Nine) for Seven, Three (of Five) for Hugh, One (of One) for One. But to specifically identify itself an individual drone will give its full function as well; Seven of Nine, Tertiary Adjunct of Unimatrix 01).
Having no regard for individuality, Borg drones were identified with designations rather than names. A drone's designation typically described its position within a group, e.g. "Third of Five." To more specifically identify a drone, its function could be appended to this designation, e.g. "Seven of Nine, Tertiary Adjunct of Unimatrix 01." In the same manner, the Borg refer to alien species by number rather than by name. Memory Alpha
DVK, I think the "smallness of address space" you are concerned about is the answer, as shown in VOY 6x02, Survival Instinct.
During that episode, Seven of Nine and 3 other drones are stranded and disconnected from the Collective. If I recall correctly, one of the things Seven does while they are stranded is to reassign their numbers to (1-4) of Four.
The "Nine" in Seven of Nine is simply the number of drones she was working most closely with when the Voyager crew first encountered her, and "Seven" is her ranking within that sub-collective.
However, I may not be recalling the events of Survival Instinct fully correctly; I know she re-linked their minds when she made the sub-collective, but I think the re-numbering happened before that.
She was the 7th assimilated person of a group of nine captured on a starship.
This seems to be the established Borg short hand naming convention going back to Star Trek TNG when we are introduced to the character Hugh.
Hugh, formerly Third of Five, was a former Borg drone who was rescued by the USS Enterprise-D in 2368. Sources: http://en.memory-alpha.org/wiki/Hugh
Hugh, or 3rd of 5, was the first such instance of being introduced to a named Borg besides Locutus (Picard's assimilated designation). When Hugh's ship crash landed he was the 3rd crew person on a ship of 5 Borg.
If the ship was not his permanent assignment then it can also be extrapolated that these naming designations were temporary, much like the IP address on your router, however this is merely speculation.
Personally i think the writers were having a bit of fun while paying homage to the early television sitcom "My Living Doll." MLD was the story of a harried scientists (Robert Cummings ) who had been charged with the enviable task of instructing another statuesque blond cyborg (Julie Newmar) in all things human. Newmar, who seemed to spend a lot of time dressed only in a towel, had the clinical assignation of " AF 709."
It wouldn't be much of a stretch to think that the writers may have been topping their caps to the show and in particular to Newmar who you may remember rocked another skin tight costume playing the original Catwoman on Batman.