Start -> end | stop | finish?

It depends.

• If calling the method will abort the task or stop it early, call it abort() or stop().

• If calling the method will wait until the task finishes, call it waitFor().

• If calling the method will perform the final steps of the task, call it finish().

• If calling the method will clean up after the task, call it Dispose() or cleanup().
  Most languages have a standard name for such a method; use it.

• Update: If I understand your situation correctly, I would recommend OnStarted() and OnCompleted()

Thats a fairly contextual question but generally you could write:

start() -> stop()
begin() -> end()

you could use finish() to clean up and close the program but close() is more used.