You guys are mixing different things by no checking the Japanese and studying their words.
Descriptive bynames like Straw Hat, Surgeon of Death or King of the Beasts are tsusho (通称) but Kaidou was talking about a rhetoric figure called makurakotoba (枕詞). Only because both can be translated as "epithet" doesn't mean they are the same; heck, even in English "epithet" has tons of different meanings.
When Oda says that the victor needs no epithets he doesn't mean that addressing Kid as "Captain" and Law as "Surgeon of death" delegitimizes their win, but that if samurai were as strong as they are claimed to be they would demonstrate it by their actions instead of their reputation.
For more information, this was my take back in the day about the makurakotoba issue:
Descriptive bynames like Straw Hat, Surgeon of Death or King of the Beasts are tsusho (通称) but Kaidou was talking about a rhetoric figure called makurakotoba (枕詞). Only because both can be translated as "epithet" doesn't mean they are the same; heck, even in English "epithet" has tons of different meanings.
When Oda says that the victor needs no epithets he doesn't mean that addressing Kid as "Captain" and Law as "Surgeon of death" delegitimizes their win, but that if samurai were as strong as they are claimed to be they would demonstrate it by their actions instead of their reputation.
For more information, this was my take back in the day about the makurakotoba issue: