There is no way of associating this Hermonax with any of those known to us. The citation is from an epigram by Antipater (Greek Anthology 6.223) and has already been given at gamma 456 (cf. gamma 457, gamma 458) to illustrate the use of this adjective for net-fishing. Antipater mentions Hermonax again at Greek Anthology 9.302, and the name recurs in the epigrams of others (9.548, 10.10). Meter requires the name to be spelled with omega, as at gamma 456; but the alphabetization here implies an omicron, which Adler prints.
[1] Here ei(=le; ei(=lke at gamma 456.