In the Old Testament of the Bible, God does have a name. The problem is, it is represented in ancient Hebrew by the letters YHWH. It was usual practice at the time to omit vowels, but it does present us with a problem in the modern age; namely, that we don't know exactly how to pronounce the name in spoken language. It is usually vocalised these days as "Yahweh", although "Jehovah" is an alternative that was more popular in earlier times. However, "Yahweh" is a sort of best-guess. There's no guarantee that it's not meant to be "Yohwoh" or maybe "Yihwah".
The translators of the King James Bible in 1611 didn't know how to render it in English and so as not to cause offence by getting it wrong, they simply rendered every occurance of it in the Old Testament text as "the LORD". Islam also considers the Old Testament to be holy scripture. I assume the hard line some Muslims take with anyone who tries to ascribe a vocalised name to God is a result of the very same uncertainty about exactly
how to vocalise it and an assumption that it's better not to try.
Incidentally, the Jews at one time were equally forthright in their insistence that nobody should try to say "Jehovah", little knowing that one day it would prove a comedy goldmine for John Cleese et al.
