The name of Alphonse Elric in Japanese is a play of language regarding the nature of the character. In Japanese, his nickname is adapted into the katakana "Aru" to mimic the pronunciation of "Al," but the hiragana "aru" (pronounced exactly the same) is a verb meaning "to exist." The Japanese, however, have two verbs for "to exist;" one for animate objects (iru) and one for inanimate objects (aru). Since a major theme of the anime is whether or not Alphonse still exists as a person with his soul affixed to the normally-inanimate suit of armor, the choice of naming him takes on a deeper meaning with this background. This wordplay could in fact be only a coincidence and not an intentional decision, but it serves as an interesting look into the nature of the language nonetheless given the theme of Al's struggle to define what he has become.

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Of course, that doesn't mean those writing his name in English should be using a Japanese word, especially if they don't know what the fuck they're actually referring to. I use "Al" because they are speaking an Indo-European language, and therefore the Japanese wordplay has no meaning. It'd be like calling Al "Exists" or something to that extent. The wordplay simply doesn't transfer in English, and therefore his English name should be used.