As can be seen from the track listing of the original soundtrack (just serving as a nice overview) a lot of names are different in the Japanese and English version. For example, Aegir/Egil, Xanthe/Zanza, Fiorung/Fiora but also Shuruku/Shulk (massive spoilers). While I still get it with Fiorung (which doesn't sound like a female name, while Fiora does) the other examples are less apparent — e.g., why Zanza, not Xanthe?
Is there a documented reason behind this decision?
Most of those actually look like the same name with me, but written in Japanese. This is a common phenomenon with media translated between the two.
For example, lets look at the name "Shulk". Well, we want Japanese players to have a decent time pronouncing the name so lets make sure they can.
Oh dear. our voice actor can't pronounce the letter L, because in japanese the english letters R and L are covered by the same letter. This means his name sounds like "Shurk". But there is another problem. Japanese doesn't have a "urk" syllable. To get around this, they add a small vowel sound between the letters to turn it into "uruk". Finally, japanese ends words with a vowel sound, so the last 'u' gets added in, giving you Shuruku.
The same process occurs in reverse
That means the names are in fact the same, they are just the Japanese pronounciations of the same names. The same rules pretty much apply for the other names, they are adjusted to make them natural to pronounce in each language.
Generally you shouldn't identify these as being "different names" but rather being different ways of spelling the same name because that name is pronounced differently. I would say they are both meant to represent the same name, and one has just been "translated" just like any other word.
It seems that, rather than just plain transliteration or translation, sometimes the localization team opts for a name which sounds better (or makes a more obvious correlation) when spoken in English. Take Karuna/Sharla for example: her name would sound too much like "Karma" if it was left as close to Japanese as possible. At any rate, the "altering" of names is a kind of constant when localizing Japanese games; such as Elza being renamed Zael in The Last Story, Ende and Ceres being renamed Aeron and Elena in Pandora's Tower, or even Azure renamed Inigo and Aqua renamed Azura in the most recent Fire Emblem games (Awakening and Fates, respectively). Truth is, there seems to be no pattern to the translation/transliteration/adaptation of names from Japanese to English, but the names' context is maintained when a simple adaptation/translation isn't possible or desirable. One can only guess, however, at specific reasons why names are translated the way they are (save for Ice Climbers "Popo", which was renamed "Pepe" in Germany because of his original name's meaning in German).
