While Hogwarts book of names would probably be cheaper if it could be accessed through the room of requirement I could see it possibly be built via the goblins as I have seen fanfiction saying they link the vault holders to the keys and have books record when the owners die and the keys no longer working - the goblins strike me as the type not to get rid of anything they could use or possibly make money on - family tree creation could be built on such a thing as their records would contain family vault creation and access so when a child is given access to a family trust vault or one is crested for them is recorded including birth data and naming of the child and the parents of said child followed by the vault records of that child until they die etc
Meaning the Goblins could build a reasonable and accurate family tree from that data and it would be a big money earner as it would take time to build the tree and in addition they could charge extra if the spouses family was also recorded back a few generations meaning spouse recorded with only their remarried name included eg Lily Potter nee Evans or possibly the parents names as well because of Lily had a vault created for her while underage her parents would have to arrange it etc this would cover Muggleborn as no one expects magical ancestors for them.
Truthfully If I was the Goblins I’d have small vaults about the size of a small room which given Wizard space means a door in a wall with about a foot behind the door then expanded into a room with fairly cheap rental for Muggleborn to obtain basically for them to both save wizarding money in and store their magical things such as old magical textbooks and notes or anything else magical they buy but are not using at that moment as a security against breaching the statute especially given many Muggleborn get tossed out of their home as soon as they are old enough. If the child knows this is going to happen they would also be storing other things in there such as copies of their birth records and muggle paperwork plus family records and photo albums so they don’t lose their past when their family throws them out when they get to a certain age.
Plus if the Goblins were canny enough such small vaults for Muggleborn could be subsidised under a protecting the statue thing.