In order to count as LTFF it has to be descended from the current LTFF and serve basically the same purpose, that purpose being to fund longtermist/x-risk mitigation projects in the ~$1k-$500k price range through an open application, and to not be OpenPhil.
For the sake of resolution, LTFF would still be LTFF if it...
changes its name
goes through a Ship of Theseus-like transformation where every role gets handed to a new person throughout the year
splits into an AI safety fund and a biosecurity fund
And would not be LTFF if it...
shuts down and somebody who used to work there starts a new fund that serves the same purpose
starts a new AI safety fund and later the original LTFF shuts down but many of the same people work at the new AI safety fund
gets eaten by OpenPhil
Let me know if I'm missing any other plausible scenarios!