Let's look at the katakana, followed by the syllables that make up each kana, followed by the name it apparently translates into:
レイム = Re-i-mu = Reim
リアム = Ri-a-mu = Liam
Now when I write about this guy, should I use Liam or Reim? I have been using Liam, since it seems a reasonable name for someone in pseudo-Victorian era pseudo-Europe to have. Most of the other characters have European sounding names, like Vincent, Gilbert, Alice and so forth.
But the name used in the actual Japanese manga text is レイム, which is Reim.
Since (to my recollection at least) Liam/Reim has not appeared in an officially translated manga or anime yet, it will be interesting to see how his name is translated/subtitled in upcoming books/DVDs. (BTW the official subtitled DVD is being released by NIS America at the end of October).
I'll keep using 'Liam' for now, but I do think 'Reim' is far cooler.