Level one: Daimon sounds like a Digimon name
Level two: Dai is Japanese for great, and if you haven't noticed Masaru is the fucking best, just ask him, he'll tell you
Level three: (Here we step into hearsay and speculation, I haven't fact checked this, so somebody tell me if they can find a source one way or the other.) Greymon is, as with many Digimon names, poorly transliterated. It wasn't meant to be the color Grey, but the "grea" from Great, meaning Savers is the story of Daimon and his Dai Mon, Daimon.
Level four: Agumon calls him Aniki, asides from the obvious Yakuza thing that carries over to general Japanese Tough Guy archetypes, but also because when he's GeoGreymon, they have the same name. They're brothers.