Sure, but that's a vacuous observation. X being determined by Y is only useful when X and Y are somehow distinct. Simply having two different labels for the same object is not very interesting.

I would suggest that if one label is singular (the world) and the other is plural (the totality of facts) and you explain how the latter combine to form the former then the observation should be especially informative.

In general pointing out that two labels point to the same object can be very informative and this is relevant for the context in which Wittgenstein was writing https://en.m.wikipedia.org/wiki/Frege%27s_puzzles