Is there an example of patrynomics in the Scylla and Charybdis portion of The Odyssey?
Yes, there is an example of patrynomics (forming the last name of a child from the first name of the child's father).
Homer refers to the sun god Helios as “Helios Hyperion.” Helios is the son of Hyperion, a Titan and also a sun god (a bit confusing). Hyperion is married to his sister Theia (or Euryphaessa), who is also a Titan. Their children are Helios (sun), Selene (moon), and Eos (dawn).
Here’s the relevant text from the Scylla and Charybdis section of Book XII:
. . . next we made our way to the excellent island
of the god, where ranged the handsome wide-browed oxen, and many
fat flocks of sheep, belong to the Sun God, Hyperion.[Book XII, ll. 260-63; Lattimore translation]
. . . Come then, let us cut out the best of Helios’s cattle,
and sacrifice them to the immortals who hold wide heaven,
and if we ever come back to Ithaka, land of our fathers,
presently we will build a rich temple to the Sun God, Helios
Hyperion . . .
[Book XII, ll. 343-47; Lattimore translation]