Some random thoughts.
1) Since "King" is basically an epithet made up by Kaido I think it is highly likely it is the same for Q&J. After all on the roof Kaido said that Jack was a strong calamity he handpicked. So there could have been a scene where Kaido went and said "You are strong, call yourself Jack/Queen and join me".
2) King is the only calamity who fully lives up to his moniker imho. Jack was terribile, at this point he should have just been called the "earthquake", at least it would've made more sense. Queen was ok, but it was clear from the moment Sanji destroyed his best protections against poison (the RS) that Queen's plagues would play no role in 1v1 settings. King on the other hand could drop a couple of those magma dragon on the fire capital and it burns down everything fairly quickly, and we know his fire also works in a 1v1 setting.
3) Kaido & young King.
Great to see he was there from the start and wants to make Kaido the PK.
4) Kaido's lore knowledge is insane. Knows about Joy Boy, knows about Robin and Pudding abilities to read PG, knew King was a lunarian and was very valuable from the start, knows about GV since he was there, and there is something else he knows that explains why he's in Wano that we haven't been told yet.