From what I know/have read,
Ruth in the Bible is simply the way the translators transliterated it, being without a pronunciation guide, and
Reut is the modern Hebrew pronunciation. Because the 'e' is a rather miniscule sound, it was left out in
Ruth, and the 't'/'th' is the same letter: there is no way to tell the difference (that I've ever heard of) in ancient Hebrew. So
Ruth is the English, like
Jacob for Ya'acov.
I dunno, I just thought that there should be some link between the two.
Y :)