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I would assume that as the Vulgate (for point of reference, the Church now uses the Sixto-Clementine or Clementine Vulgate, the 1592 revision of St. Jerome's Vulgate) is a translation of Greek and Hebrew texts into Latin, the corresponding Latin words would be used.

From some quick "look-it-up": Yahweh and Jehovah are older English representations of YHWH.  The only English bible I know of that uses the word "Yahweh" in the Old Testament is the Jerusalem Bible (it's revision in the late 1980's is the New Jerusalem Bible).  I did a quick check of a few passages where Yahweh is used in the New Jerusalem.  In the Vulgate it is translated as Domnius and in the Douay-Rheims (Bishop Challoner revision) it is rendered as Lord.

I assume you're just curious, so please don't take this personally.

Knowing Anthony (only from his posting), I imagine he's just asking why and not questioning its validity.

Prots try to turn Yahweh into some proper name, but the entire point of the expression by God was to say that He HAS NO NAME.  Names define the essences of things, but God has no essence, only an existence, so to use "Yahweh" as if it were some kind of name directly contradicts what God was trying to reveal when He said, "I am Who am."  Nevertheless, a designation for "I am Who am" (as referring to God) needs to be there as a placeholder for its appearance in various grammatical constructions, so the Hebrews inserted "Adonai"  in place of Yahweh when reading or explicating the text, since the Divine Name (or, rather Non-Name) was ineffable and unknowable.

So, the bottom line is that it's a mistake to think of "Yahweh" as some kind of name, or, as you put it, the "Divine Name", when it's really a Divine Non-Name, i.e. a reference to God denying that He has a name at all.