In the article Book of Mormon Names Attested in Hebrew Inscriptions by John A. Tvedtnes, John Gee, and Matthew Roper, we read the following:
Patristic Names
A feature of the Book of Mormon that is unknown from the Old Testament is the naming of a son after his father. Thus, we have Alma son of Alma, Helaman son of Helaman, Nephi son of Nephi son of Helaman, and Pahoran son of Pahoran. Until recently, patristic names of this sort were unknown from epigraphic sources. But an ostracon from the late seventh or early sixth century BC in the Moussaeiff collection lists one ʾlkn bn ʾlkn, “Elikon [or Elkanah] son of Elikon.” (See Robert Deutsch and Michael Heltzer, New Epigraphic Evidence from the Biblical Period (Tel Aviv: Archaeological Center Publication, 1995), 89–90. 14)
While browsing through a volume that arrived in the mail today, Gary J. Johnson, Early-Christian Epitaphs from Anatolia (Texts and Translations 35; Early Christian Literature Series 8; Atlanta: Scholars Press, 1995), there are other examples, albeit post-New Testament, of patristic names. Such should not be taken as an attempt to provide evidence for Book of Mormon antiquity, but instead, to show the antiquity of the practice, and that such is not a wholly modern phenomenon.
In a stele from Izmit/Nikomedia (p. 10):
Δειος Δειου
The Greek means “Deios son of Deios" (lit. "Deios of Deios").
In a sarcophagus from Izmit/Nikomedia, we read the following (p. 12)
Αιμιλιαι Παυληι Αιμιλιου
Παυλου θυγατρι
Παυλου θυγατρι
The translation offered on p. 13 for the above is:
For Aimilia Paula, daughter
of Aimilios Paulos
of Aimilios Paulos
What is interesting is that, in this instance, the father gave the feminine form of his name to his daughter, adding a twist, if you will, on patristic names.