🔼The name Bazluth or Bazlith in the Bible
There's only one person in the Bible named Bazluth, and according to Ezra, he's the patriarch of a family that made it out of the Babylonian exile and back to Canaan (2:52). Ezra's contemporary Nehemiah also makes mention of this person, but he calls him בצלית (Bazlith — 7:54).
It's not clear how this name ended up in two different spellings but it may very well be that Ezra and Nehemiah were the first ones ever to record this name, and the rendering is phonetically (and somewhat depending by the accent of the one who's reporting). But it's essentially the same name, and the difference may be compared to, say, that between Rebekah and Rebekah.
🔼Etymology of the name Bazluth or Bazlith
The name Bazluth or Bazlith comes from the assumed root בצל, possibly meaning to strip or strip off:
It's quite a leap from the verb בצל to our name Bazluth or Bazlith, but the yod-teth extension may be due to a common grammatical form, and the letters yod and waw may interchange.
🔼Bazluth or Bazlith meaning
For a meaning of the name Bazluth and Bazlith, BDB Theological Dictionary and NOBSE Study Bible Name List both read Stripping. Jones' Dictionary of Old Testament Proper Names proposes the flowery A Making Naked.