His name looks like it should be from the adjective ἄξῠλος 'woodless', but the quantities differ. He must have a Kurzform of a name in Ἀξι- (cf. names in -αξος), built with -υλος (Schwyzer, GG 485.2). For these names, see the tables below (with thanks to the LGPN online search).
See Hans Von Kampz, Homerische Personennamen (Vandenhoeck & Ruprecht, Goettingen: 1982), § 46c (p. 130), who compares Ἥγυλλος (to which add Ἅ̄γυλλος) and Ἥγυλος (to which add Ἅ̄γυλος) as shortname forms of Ἡγέ-στρατος.