To see why His Name is pronounced "Yahweh" I would point you to the following resource which I have checked out thoroughly and have found to be adequate and in agreement with what I have found on the pronunciation. I do not necessarily endorse the views of the author in other topics presented in this book or in other books by this author.
This is a chapter from the book entitled "The Sacred Name" by R.CloverLately, I have noticed that there are many using the form "Yahuah" or "Yahuwah" based on the fact that the Name יהודה "Yahudah" (Judah) contains the same letters as with the exception of the ד Daleth (D) being added (Hebrew reads from right to left). In other words, Yahweh's Name contains (Yod Heh Waw Heh) and the name of one of the sons of Israel (Judah) is יהודה (Yod Heh Waw Daleth Heh.)
They say that the Heavenly Father's Name can be "made simple" by learning that since there is only one letter difference between the two names, we can learn the pronunciation of the Heavenly Father's Name by looking at how Yahudah's name is pronounced in Hebrew.
But the truth is we cannot determine the pronunciation of one Hebrew word by looking at how another word is pronounced with similar letters. In Hebrew there are numerous words that have only one letter difference but they are pronounced completely different.
A couple of examples in Hebrew as it relates to Yahweh's Name:
יהצה #3096 is pronounced "Yatsah" in Hebrew. This is in contrast to יהודה "Yahudah" which is only one letter different.
The verb Hama (#1993) is found in Jeremiah 6:23, 48:36, 50:42 in the qal imperfect 3rd person masculine singular form, and is spelled יהמה but pronounced "Yehemeh." Again, this is in contrast to יהודה "Yahudah" which is only one letter different.
Notice that there is only is only letter difference between those words and יהודה but they have vowels which are not the same. If we removed vowels from two English words that had similar consonants, no one would argue that we can figure out the vowels of one by knowing the vowels of another.
If the "Yahu" in "Yahudah" is in reference to Yahueh/Yahuwah (and this is not certain), the "dah" comes from a different Hebrew word, so we can't rely that to arrive at the correct pronunciation of .
In fact, there are examples in Hebrew where two completely different words are spelled exactly the same way, but are pronounced completely different. The word שאול, which is pronounced "Shaul" (King Saul's name) is spelled exactly the same as the word שאול, pronounced "Sheol." "Shaul" means "desired" but "Sheol" means "grave." The vowels are completely different, but the word is spelled the same.
The reason why Yahweh's Name is upon His people is not because "Yahudah" contains part of Yahweh's name as some claim. Yahweh's people are called by His Name because of the elements seen in the priestly blessing:
Numbers 6:24-27, 24Yahweh bless you and keep you; 25 Yahweh make His face shine upon you, And be gracious to you; 26 Yahweh lift up His countenance upon you, And give you peace." ‘27 "So they shall put my Name on the children of Israel, and I will bless them."
So in conclusion, to base the pronunciation of the Heavenly Father's Name on how another name or word is pronounced is not sound reasoning and should be completely disregarded when seeking to understand how is pronounced.
Also, it is important to understand that in Hebrew, the verb form determines how the vowels sound. This is not unlike English where the verb "Run" changes to "Ran" if past tense is intended and "Running" if present tense is intended. In Hebrew, the vowels sounds will change depending on whether it is 1st, 2nd or 3rd person, or whether it is masculine or feminine, etc.
In Exodus 3:14 Yahweh said to tell the people of Israel that His name is "I AM THAT I AM" or "Ehyeh asher ehyeh." We know that "ehyeh" is the way you pronounce "Hayah" (a verb meaning, "to be") in the first person form.
Why then did He say to call Him "Yahweh" in Exodus 3:15? The form "Yahweh" is the 3rd person form of the same Hebrew verb, "Hayah." Yahweh was declaring who He is in saying "I AM" ("ehyeh") but when we say "Yahweh" we speak of Him in the 3rd person form.
Why the Name of the Messiah is spelt and pronounced Yahshua
The name of the Messiah, in Hebrew-His own language, is , which means "Yahweh is salvation" or "Yahweh saves". The name "Jesus" is the result of a series of changes from Hebrew to a Latinized Greek. The word is not a transliteration, and it cannot be translated, since it is a hybrid word.
Hebrew names can be translated; they make a statement, such as, Yahshua = "Yahweh is salvation". The word "Jesus" does not deliver the message that Yahweh is salvation. [and, of course, "Jesus" was never actually his name.]
The pronunciation of varies among different groups. Since the Hebrew spelling is exactly the same as "Joshua", the son of Nun, some people pronounce it as "Joshua" with a "Y" sound - Yahshua; the "Y" would be the correct sound since the "J" sound does not exist in Hebrew. In fact, because of the same spelling, the King James Version mistranslated Acts 7:45 and Hebrews 4:8 using "Jesus" instead of "Joshua" (other versions like the NIV have corrected this). In reality, the name of Joshua and the name of the Messiah were the same name.
Stong's Concordance states that #2424 - Iesous is of Hebrew origin #3091 - yeh-ho shoo'-ah; and that this is also the name of Joshua, the Jewish leader. Some people state that the ancient pronunciation of this name is Ya-HO-shu-wa, and that by the time of the Messiah, the "HO" had been dropped; I have seen no written study or evidence of this. Strong's has obvious errors, "Yeh" instead of "Yah." His vowel points are of more modern Hebrew usage; he uses a sheva instead of a pattach and thus gets "Yeh." And, he uses "Jehovah" instead of "Yahweh."
We can understand, now, that "Jesus" would not have been the name that Miriam (Mary) was told to give her son. The "J" sound didn't exist then, and doesn't exist now, in the Hebrew or Aramaic languages. In fact, it didn't exist in English until 500 years ago.
Matthew 1:21 And she shall bring forth a son, and thou shalt call his name Yahshua (means: Yahweh is salvation): for He shall save His people from their sins. 22 Now all this was done, that it might be fulfilled which was spoken of the Master by the prophet, saying, 23 Behold, a virgin shall be with child, and shall bring forth a son, and they shall call His Name Emmanuel, which being interpreted is, EL with us [means: a mighty one is with us].
"Yeshua" is the name used by today's Jews and messianic believers when referring to the Messiah. The "Ye" was a replacement of "Yah" to avoid pronouncing the Father's name even in its shortened, poetic form [a traditional Jewish restriction that began at the time of the Babylonian exile]. Using Yeshua does not honour Yahweh as intended in Matthew 1:21 above. By pronouncing Yahshua, we state that Yahweh is salvation.
Yahshua is Yahweh Manifest in the Flesh!