In the Hebrew Scriptures
The Tetragrammaton appears multiple times in the Hebrew Scriptures. Many translations render this as LORD, following the Jewish practice of not pronouncing the Divine Name (though the Jews do write the name in their scriptures). The Jerusalem Bible renders the name as Yahweh, which is a scholarly “best guess” at the original pronunciation. The New World Translation uses Jehovah, which is almost certainly not the original pronunciation, but is the traditional rendering in English, found in both religious and secular books for many many years. Certainly including some form of the name is more accurate than bowdlerising it.
As for the decision to use that specific rendering: Why not? Names change from language to language. If we’re happy to see Rebecca, Solomon, and Jeremiah in our English translations, why not Jehovah? (This especially applies to names like Jeremiah, which include a reference to the Divine Name. Having both start with J makes that more obvious to the English reader.)
So, the name is there, in the text, and the translation includes it. Translations which leave it out are the ones which need to explain themselves, not the ones which leave it in.
In the Christian Greek Scriptures
The New World Translation also uses the name Jehovah in the Greek Scriptures, although it is not found there in any extant manuscript. When the Greek text quotes the Septuagint, they reinsert the name (yes, reinsert, as they maintain that it was there originally). Certainly there do exist editions of the Septuagint which contain the untranslated and untransliterated Tetragrammaton, and others which render the divine name as Pipi, suggesting that they were copied from an earlier version which contained the original Tetragrammaton, the Hebrew letters of which look a little like the Greek letters for Pipi. So, where the Christian scriptures quote passages from the Septuagint, it is somewhat reasonable to assume that the Tetragrammaton, or some variant thereof, existed in the original text and was later lost.
Somewhat reasonable, yes. but only somewhat. The fact is that no form of the Divine Name exists in any extant manuscript of the Christian Greek Scriptures, the belief of the New World Translation Committee that it was there origionally notwithstanding.
However, NWT includes the divine name in places where the Christian text is not quoting the Septuagint. Sometimes support comes from the existence of the Tetragrammaton in Hebrew translations of the Christian Greek Scriptures (some of those Hebrew translations used for support are actually fairly recent, so any support they offer is tenuous at best). The name Jehovah occurs many times in the New World Translation of the Christian Greek Scriptures, each time accompanied by a footnote and an explanation of the rationale in The New World Translation — with References.