He doesn't have any particular objection to introducing himself to any of Shaxx's circle, but there's a precise difference between introducing himself and being himself. Despite his time and efforts in Sumarlok, Daigo is really no better at taking off his armor sometimes. Maybe no one calls him that anymore, but the chairman lives and breathes.

"Of course," he was never going to say no. "It would be customary to take you all out on the town, even."

That's how the yakuza do it, anyway. Your sworn brothers people are your people and they receive the same hospitalities. Although, usually the scene is that your brother has been in jail for however many years, and that is why you're celebrating finally seeing him again.