The ones that D.B. hosted in AW that I eventually started CMing was called the ThunderDome Tournament, with the premiss "many will enter, but only one will leave". Those were a regular monthly special event.
Many other tournaments were one-offs and were named by their sponsors (eg. AWCenter P38J Tournament).
Just throwing some name ideas out...(trying to avoid the word 'ladder' since that usually indicates a challenge system rather than a
knockout tournament)
ToF Tournement of Furballers
FDT Fighter Duel Tourney
AHKoT Aces High Knockout Tournament
FUR Fighters (or Furballers) Ultimate Rivalry
(had to find a way to get "FUR")AHFE Aces High Fighter Elimination
CoD Clash of Duels
CoF Clash of Fighters (or Furballers)
AHDT Aces High Dueling Tournament
Less utilitarian names
AHTD The ThunderDome

AHPG The Proving Grounds
AHFS The Fighter Showdown
KoTD King of the Duels
Agreed upon pre-merge alt. (future map will have bases @ 2k, 4k, 6k etc)
Hard cap pre-merge. (i.e. 4k agreed upon, no climbing over 4k b4 merge)
No firing 1st pass.
30 sec. extension limit. (after 30 sec you HAVE to turn and merge)
Best of 5 wins.
That was pretty much the rules we used, with a redo clause for warps that "materially affected the course of the fight", and discos after the first merge counted as a loss.