Okay so what I've gathered is this:
Nekos are born in small groups with identical last names: i.e. out of a production of 250 nekos there will be ~60 different family units.
The names are usually chosen from a pool of pre-approved last names, which is unique to each installation. Sometimes a techie (their creator) can give them his/her last name as well. Or possibly their own last names are included in said pool.
Like modern times, it isn't required that the neko keep the assigned last name, and it is capable of being changed.
Question Revisited and Revised
Given the above information, we could assume that nekos are in fact born in families, albeit a unique family, thus should this information be included in some part of the NH-29 wiki for new players who wish to incorporate this into their character? This could be an interesting way for some nekos to be related.