Homer appears eleven times in the Greek Anthology as Maeonides (in Doric Maeonidas, as here), and these are two of the instances. The first (7.213.7-8) is by Archias, probably the poet for whose claim to Roman citizenship Cicero delivered his speech In Defence of Archias (pro Archia). The second (7.2.1-2) is by the prolific Antipater of Sidon.
Maion/Maeon's claim to paternity is perhaps based on the tale told by Ephorus of Cyme in his Story of his Native Land (FGrH 70 F1), that there were three brothers in Cyme, of whom one, Apelles, entrusted his daughter Kritheis to another, Maeon, who deflowered her and, to avoid the scandal of her incestuous pregnancy, gave her in marriage to a verse teacher in Smyrna called -- Phemius! In the surviving "Lives" of Homer (all from Roman times) Maeon becomes the eponymous founder of the Maeonian people (who adopted Homer according to Aristotle, fr. 1.11.7b.13), an Amazon or a respectable citizen of Cyme. It is interesting to speculate that Homer might have been the son of "the Maeonian", referring to the people who preceded the Lydians inland from Cyme and Smyrna, from whom the Etruscans claimed descent and who are identified by Eustathius with the Dardanians (on the Trojan warrior Maeon at Iliad 4.394). Maeonides or Maeonius becomes a favorite name or adjective for Homer and Homeric in Horace, Ovid and other Latin writers. Vergil attributes the name Maeon both to an Etruscan and to a Trojan. This may mean that the name is a poet's compliment to Roman Etruscans such as Maecenas (mu 321).
For the story of Homer's death on Ios, after he could not solve the fishermen's riddle, see omicron 251 (end). Homer did not, to the best of our knowledge, write hymns, but we have surviving 'Homeric Hymns', at least one of which was by a Homerid 'follower of Homer' and designed to be sung as a prooemion (introduction) to his work (Thucydides 3.104, apparently attributing it to Homer).
[1] The word gri=fos originally meant 'fishing-basket, creel', and was probably extended by Aristophanes and others to mean 'riddle' and even 'penalty for not answering a riddle' (Hesychius: see LSJ), by allusion to the story of Homer's death. See gamma 457, gamma 458. Archias clearly here puns on the two senses of the words.
[2] Greek Anthology 7.2.1-2 (Antipater of Sidon), on the tomb of Homer in Ios; see Gow and Page (vol. I, 14), (vol. II, 40-41), and another extract from this epigram at phi 115. With its eponymous polis, the Cycladic island of Ios (Barrington Atlas map 61 grid A4) is located about 25km south-southwest of Naxos (cf. nu 27).