I find the Icelandic (Scandinavian?) tradition appealing, where surnames are either father's son, or mother's daughter.
That's a general, ages-old Germanic thing, but it has gone out of fashion everywhere else besides Iceland after the 19th century - at which time even the most barbaric corners of the Nordic nations began to have universal taxation and thus also universal records which more or less required the invention of surnames. Sometimes, the last iteration of patronymics would get turned into a surname for record-keeping purposes, so Hansson or Jensen would become a "true" surname, now to be carried by all
the following generations even if the father was named Olaf or Sven or something else than Hans or Jens.
Whether Vulcans would be worried about things like tax records, or whether they'd be perfectly happy about having six hundred guys with identical names populating the planet at any given time, is unknown. We get lots of coexisting T'Pels in Star Trek, but we never learn if they have a distinguishing element to their names. They might just as well live without, there never being anything unclear about who was the wife of whom. (Or if there was, there'd be an ancient ritual involving lots of violence that would solve the problem to logical satisfaction.)