User blog comment:Crimson and Darkness/Volume 24 discussion blog/@comment-30924344-20180101234213/@comment-2601:8C:601:5692:8493:9949:ADF9:B1B2-20180103095324

The actual name of Dulio's team is "Joker of Heaven" or "Heaven's Joker", depending on your preference. The  切り札 part has the intended reading of "Joker" despite the kanji translating as "trump card", the other part (excluding the 'no' hiragana that tls as 'of') reads as 'tenkai' an simply tls as "Heaven's.

As for Typhon's team, going directly by wiktionary it would translate as "the frolicking of kings", but that sounds bad and most of the other suggestions fit as well, though some are a little more poetic/take artistic liscense. I personally would choose either the "Sport of Kings" or the "Amusement of Kings" from them. Mind you, the can alternately be read as "Kings' Sport" and "Kings' Amusement" as well. Whatever the case, what should be conveyed is a lack of seriousness. For its members, this is truly just trivial leisure play, trifling amusement. Another from GoogleTL was "Kings' Dalliance", but I'm a bit iffy about this one. The biggest problem is that none really sound all that great as a team name.