No, hold on, those two things aren't remotely the same.

It makes sense to work out which kid belongs to which parent, for sure. For one thing, a whole bunch of the legal system is based on who inherits what when people die. You want some way to keep track of that. There's some weirdness about keeping track of the father rather than the mother, and some cultures keep track of both or of the mother first, which makes more sense, but that's a different conversation.

But "who's paired up with who"? Absolutely not. Why would it be more convenient to be unable to separate sexual partners from descendants? That is not a practical thing. And the stuff that's preserving, which is that women are historically treated like children without full legal autonomy and part of the stuff being managed by a paterfamilias, is fortunately no longer true.

And of course once that gets recognized enough that even a bunch of Christianity admits that not all relationships are forever and reintroduces divorce (after centuries of treating women like perpetual property of their husbands) it makes absolutely no sense to have half the population ping-pong between names over their lifetime an arbitrary number of times. It's not only logically absurd, it is actively inconvenient to both the first goal of pairing descendants but also administrative bookkeeping in general. I can only imagine the amount of public records errors induced by women changing their name a bunch of times over their lifetimes.