Just realised out of all the factions recognised by New Japan, only LIJ has an outright leader

I'm going by the factions officially recognised by New Japan in the faction videos they release periodically:

LIJ – Naito

Chaos – no leader designated since Okada left

United Empire – TJP is the "captain" but commentary has differentiated this from him being the leader. My guess as to why is that in kayfabe the members of UE probably still regard Will Ospreay as the leader, even if this has never been blatantly stated within storyline

TMDK – ZSJ is the standout wrestler in the faction but they've specifically stated there's no leader

J5G – Sanada is the standout but they've also specifically said there's no leader

Bullet Club – Finlay calls himself the leader of BC but doesn't recognize other aspects of the faction like House of Torture or some as not as important as War Dogs (ie: Ishimori, Kenta and Chase). House of Torture, War Dogs and the Rogue Army effectively operate independently under the Bullet Club banner

I just find this quite interesting since until a few years ago it was an extremely important position in the way New Japan presented it's story, since it was pretty much only leaders of their respective factions that were considered viable contenders for the IWGP HW Title