Your question is asking about a name, and the names of ideas in physics are often historical accidents that have little significance. So in general it's a bit pointless asking why a particular name was chosen.
In this case the name principle of least action is actually appropriate - well almost. It's because for any trajectory we can calculate the action and then we find the trajectory for which this value is least. Hence least action.
I say almost because we actually extremise the action i.e. it can be a minimum or a maximum, but as I said the names for things in physics are often not especially appropriate. Anyhow, principle of extreme action sounds like a gangster movie :-)