In (VOY: "Collective"), Seven of Nine retrieves the children's names from Borg's assimilation profiles. Why would the Borg keep such individual-related profiles? How do they manage to record such profiles when a mass assimilation of billions is carried? At what stage of assimilation do they access one's biography and record it?
The Borg are information addicts
So when a species or population is assimilated, they are injected with self-replicating nanoprobes that infect the host organism. Upon infection, one of the immediate functions of Borg nanoprobes is the construction of a neural transceiver which links the host individual up to the hive mind—a virtual network of the minds of all Borg drones connected via subspace (sort of like a distributed computing cluster), resulting in a single collective consciousness.
The more species and populations are added to the collective, the more advanced/intelligent/powerful the Borg become. Although drones are robbed of their individuality, their creativity, their personality, etc., the experiences and knowledge of each drone feed the Borg's ability to improve itself, to adapt to threats and to strategize.
This is how and why the Borg assimilate. So it wouldn't make much sense for the Borg to just toss out the valuable knowledge and experiences of their drones — which is arguably a far greater prize than the physical technology they capture.
The Borg isn't interested in wanton destruction and much prefer efficiency over waste, so you'd expect them to save and catalog every bit of information they come across.
The Borg cluster has plenty of storage
As to how it's possible for the Borg to retain the knowledge of every individual they assimilate using the brains of every individual they assimilate? Well, just because you obtain a billion hard drives and shuffle the data around between all the hard drives and re-organize the data, doesn't mean the volume of the data has changed. Remember, the Borg don't really synthesize original knowledge on their own. They are almost slavishly dependent on assimilation for acquiring new knowledge and only recombine or make incremental improvements on assimilated research/technology (e.g. the Omega particle).
And that's before you even take into account the cybernetic enhancements that Borg drones receive, which allows Seven of Nine to become possibly the most advanced/intelligent (or at the very least the most knowledgeable) human alive in the 24rd century (with the exception of One and Reginald Barclay while he was under the influence of Cytherian control).
I suspect it's more of a side-effect of assimilation, than anything else.
In the flashbacks in VOY 6x02, Survival Instinct, we see 4 drones all start to remember who they are once they're disconnected from the Collective. Their memories weren't ever erased, just suppressed.
When a drone is assimilated, they're given a cortical implant, which allows their mind to interface directly with Borg technology. The cortical implant can also store neural patterns, as seen when a damaged vinculum started to bring those personalities to the surface of Seven's mind in VOY 5x07, Infinite Regress.
The personalities Seven experienced had to come from somewhere, either long-term storage in Seven's cortical implant or directly from the vinculum itself. Either way, it would seem that the minds of assimilated drones are stored in computer systems, which means their memories should in some way be accessible from Borg terminals.
The specific information about their names probably wasn't purged due to the fluid nature of the Collective. It is made up of the minds of billions of drones - selectively eliminating memories could have further repercussions inside the mind of that particular drone, making its contribution to the hive mind less than it otherwise could have been - and there's no way of knowing for certain that the information might not be useful later, such as the connection between "Picard" and "Locutus".
Finding, classifying, and then erasing irrelevant information would also become extra effort expended for no real benefit - a drone is a drone, not an individual. The name is irrelevant, whether or not it is remembered.
Because it makes sense to have independent records.
Seven of Nine mentioned in the episode with the Vuadwar that the collective's memories from ~900 years ago are extremely fragmented, and it's possible that this problem is also present in other eras of data as well. The Borg know this is a problem. So it makes perfect sense form their perspective to use some forms of external storage, especially if it's information you don't need very frequently, such as assimilation data of someone you already assimilated, backups, etc.