Hashem is the way many religious Jews express YHVH, the Tetragrammaton, the name of God revealed to Moses in Exodus 3. Many Jewish people will say upon hearing good news, "Baruch HaShem." Which means blessed is the name. But this is not the name of God revealed in Scripture.
Dr. David Edery points out why they use this name. It is more than the usual explanation; they do not feel worthy to utter His name. It is actually that they don't want to mispronounce His name. There is no doubt that Moses and Aaron knew the correct pronunciation of YHVH, as God shared it with Moses directly from the burning bush when he said that his name is, "I AM WHO I AM.” This is what you are to say to the Israelites: “I AM has sent me to you." But Ancient Hebrew did not have vowels. Vowels were added later to help us pronounce the words and were only finalized in the 6th century CE, thousands of years after Moses.
For a crude example, it would be like saying someone's name was Iris but pronouncing it incorrectly. In Hebrew, we pronounce that as ē-ris, not ī-ris. Arthur is pronounced one way in English, but in many other countries, it is spelled the same, but the h is silent, Ar-tur. Such a mistake is fine with mere humans, but one would not want to mispronounce the holy name for God Almighty. Orthodox Jews fear they would be breaking the third commandment.
They will say Adonai (Lord) instead Yahweh, the name God revealed to Moses. Instead of saying Elohim (God), they say EloKim. And in English, you will notice that many will not write the vowel in G-d. When preaching in Hebrew, I will simply say the Hebrew letters Yod, Heh, Vav, Heh (יהוה), since the pronunciation of the word is not known. I can't think of ever hearing anyone who is fluent in Hebrew seeking to pronounce his name.
However, we can learn something of the meaning of His name when He explains it to Moses. He says, אהיה אשר אהיה I will be who I will be. Many translate that as "I am who I am." It all comes from the verb "to be"—l'hi-ōt in Hebrew. Similar letters are in the Tetragrammaton, the four letters in God's name.
יהוה Yahweh להיות to be אהיה I will be They all have the root for the verb to be היי (https://he.wiktionary.org/wiki/יהוה)
But what does it mean?
Here is where it gets good! We can assume from God's words to Moses that His holy name has something to do with the fact that He exists and He is going to do what He wants to do. Is that not the theme of Exodus, where His name is revealed? God exercises His will over Egypt and the Children of Israel. He tells Moses that He is giving him more information than He gave to the patriarchs.
"I am the LORD (יהוה). I appeared to Abraham, to Isaac, and to Jacob as God Almighty (El Shaddai), but by my name the LORD (יהוה) I did not make myself fully known to them. (Ex 6:2–3).
And His name is something like I AM, or I WILL BE. In ancient Hebrew culture, names meant something. God changed the names some of the patriarchs for prophetic reasons: Avram to Abraham, Jacob to Israel. So, we can be sure that God's name has prophetic significance too.
We see the meaning in the outworking of the Exodus story. God proves that there are no other gods besides Him. He mocks the deities of Egypt. He slays their most precious deity—Pharaoh's son. He appears as fire at night and a cloud by day. He takes more than one million slaves through the Red Sea miraculously and changes them into “a kingdom of priests, a holy nation” (Ex. 19:6). No Pagan god ever attempted such a feat. When God wants to do something, He's going to do it. He is a strong-willed God!
That encourages me in my prayer life. If I know something is God's will, I can pray with confidence and passion, as my God has a very strong will. That is why we pray, "Let your will be done on earth as it is in heaven," (Matt. 6:10).