R Aryeh Kaplan had a fascinating article in the Jewish Observer, December 1976 (reprinted in The Aryeh Kaplan Reader, p. 74, see here) where he discusses the process used to write the first gittin in Monsey, NY involving R Yaakov Kamenetzky, R Moshe Feinstein and others.
He writes about the particular importance of getting the spelling of all names right. He refers to SA Even HaEzer 128 (see e.g., 128:2, which speaks of cities and not areas or buroughs).
R Kaplan describes how one needs a mesorah (tradition) to decide which city name to use, how to write it and how to refer to the landmarks and rivers close to it (if relevant).
As such I would imagine one writes Brooklyn because it was a city until 1898 (Wikipedia here) but London because Stanford Hill is not a city but an area of London (here). In all cases the local beit din would be the holder of the tradition on the exact spelling.