In most anime, the character's names are usually common Japanese names (for example, Yuuki, Yoko, Chiharu, etc.). So, why in Fullmetal Alchemist are the characters' names more on the English side of things?
The main setting of FMA is in Amestris, which is a pastiche of various European countries, in particular, England. (See the answers to this question for more details.) We can readily see that English is used in-universe, for instance, when Hawkeye corresponds with Roy, writing in vol. 19 of the manga:
SELIM BRADLEY IS HOMUNCULUS
Note that many character names are not actually "English" or even German, although fans often posit Amestris to be a parallel of Germany. Some examples:
Jean Havoc's first name is French -- in English, Jean is more commonly a female name and is also pronounced differently -- and Riza is possibly a Hungarian name. Olivier might sound English, but it is not an English spelling of the name Oliver.
With regards to the suggestion that the names are German, Hughes, Bradley, and Armstrong are at most rather English in nature. Similarly, the German equivalent of Jean would presumably be Johann -- see this webpage on the name.
I remember Arakawa stating she chose names at random from a dictionary of European names for more minor characters, on some of manga bonus pages. I don't remember the specific chapter where this appeared, but this is stated in one of the answers of the question I linked to and also readily comes up in search results for
arakawa european name dictionary fullmetal alchemist.
So in short: the names are not Japanese because the setting is largely in a country derived from Western Europe of the late 19th or early 20th century. However, it is incorrect to say that the names are English or necessarily German in origin. Of course, it's possible that there's so much ethnic diversity in Amestris that some variation in names isn't entirely unexpected, but well, that supports the "pastiche of Europe" view of the setting more.