From Ògún + yẹ ("befit, be worthy of") + mi ("me"): "Ògún befits me." Same òrìṣà-lineage pattern as Ogunbiyi; the -yẹmí ending also appears in Adeyemi and Oluwafemi.
Source: Yoruba òrìṣà-lineage surname, cross-referenced across the DiscoverYorùbá surnames guide and the -yẹmí compound pattern attested on Wikipedia (Adeyemi) and yorubaname.com (Olúwáfẹ́mi)