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 they 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.