Yamato is honestly a pretty curious name for Kaido's son. First because It doesn't seems Kaido is from Wano (equivalent of fantasy Japan) so stereotypical japanese for his son is odd (all beast pirates have foreign names). And because it's not a typical "bad guy" name. For example "Orochi" sounded villainous for the japanese readers even before we saw him because Orochi is the name of a legenderay and evil japanese snake monster. Kanju used for Kurozumi in the manga also lireally means "black charcoal" aka darkness.
Meanwhile "Yamato people" is how japanese refer their own ethnicty (
https://en.wikipedia.org/wiki/Yamato_people )
Yamato-damashii "japanese spirit/values/moral (
https://en.wikipedia.org/wiki/Yamato-damashii )
Yamato nadeshiko "the perfect japanese" woman (
https://en.wikipedia.org/wiki/Yamato_nadeshiko )
And depending on the kanju used yamato can mean "Great peace)
At the end it's just a name, so it could mean nothing but I truly doubt Kaido's son will just be a gag character or simple strong guy to fight for the straw hats and nothing else!