Perhaps names are assigned to children arbitrarily?
Meaning: The child who grows up as Logan 6 may not even BE Logan 5's biological son. In a system like this, what real reason would there be to actually trace family lines? There ARE no families in the city, after all...hell, I'm wondering why people in the city even have names. What's the point?
I'm even starting to suspect that births, such as they are, occur without the mother even knowing about it...the computer may have some way of extracting an embryo from the womb without any conscious effort on the woman's part. (While she sleeps, for example.) So while all this sex is going on, there are no actual pregnancies...
Indeed, when Logan and Jessica meet the old man, they act completely amazed and confused when he says he came from his mother, didn't they? It's like they've never even heard of a pregnancy. So I'm kind of doubting that women actually carry babies to term in this city.