Why use Yahweh instead of Jehovah? Maybe it is more accurate but then we should call Jesus Yashua.
"Jehovah" is criticized because it was a word derived based on a misreading and misunderstanding of the Hebrew texts.
In the Jewish tradition, going back a very long time, it was considered rather inappropriate to speak the Name itself (YHWH) and so when reading the text another word was substituted in its place,
Adonai, meaning "lord" or "master". This is ultimately also why the Septuagint, renders "YHWH" using the Greek
kurios, also meaning "lord" or "master"; and by extension the New Testament using the Septuagint retains
kurios when quoting and referencing the Old Testament.
Jewish scribes from the middle ages introduced to the Hebrew texts pronunciation marks, or vowel marks, due to Hebrew being an abjad and thus lacking characters for vowels (in other words, Hebrew only contains consonants, in writing vowels are
implied but not written); these marks are known as niqqud, they are dots and dashes that aid in pronunciation of words. These scribes, the Masortes, in order to emphasize that Adonai was to be read aloud in place of YHWH used the niqqud for Adonai with YHWH.
What this meant was that when Christian scholars started becoming more interested in translating Hebrew texts, they effectively saw the word written as YaHoWaH, the Hebrew character Vav/Waw can have a 'w' or 'v' sound; and the result was the Latin Iahovah. With the introduction of the letter 'J' in the late middle ages to replace consonantal 'i' Iahovah became written as Jahovah/Jehovah.
But the problem still remains, "Jehovah" is based on a fundamental error of reading comprehension among early Western Christian scholars of the middle ages, and only is retained generally because of it having been incorporated into some early translations of the Bible.
Personally, I usually just use what most English Bible translations do, and that is to use "Lord" (or "LORD") in common speech and writing. When quoting the Old Testament I tend to follow the tradition of using "LORD" in all caps for the same reason that I follow the tradition of capitalizing most pronouns in reference to God ("He" rather than "he", "Him" rather than "him") but such is just personal preference.
But if we're talking about the Name itself (note again the capital 'N' I gave it, again, that's just my personal preference) "Jehovah" is just wrong. "Yahweh" is really just an approximation as we really don't know how to pronounce YHWH, but it's certainly better than "Jehovah". Though I caution quite strongly against the Sacred Name Movement and their insistence that God must be called this (or some peculiar variant of their choosing) as that's ultimately legalistic nonsense.
If you want to refer to Jesus as "Yeshua" you are certainly free to do so; though I don't and don't see any good reason to as "Jesus" is a perfectly good transliteration of the Lord's name as it has entered into English from Aramaic through Greek through Latin. "Jehovah" however is just in all senses bad, it's based on a mistake; having said that if one wants to use "Jehovah" they are free to do so, the Almighty isn't ignorant of what men mean by their words. But from a purely academic perspective "Jehovah" is rather unacceptable.
Likewise, from a purely academic perspective, it may be somewhat inappropriate to use "Yeshua" as while "Yeshua" is certainly a Hebrew form of the name of Jesus, Jesus, His mother, and His community didn't speak Hebrew, they spoke Aramaic. And thus approximations have been proposed, as the Aramaic of Jesus is effectively a dead language, only Syriac remains as a living form of Aramaic.
-CryptoLutheran