By My Name of Hashem I was not known to them. (Shemos 6:3)
There is a big difference between the Name Hashem and the Name Elokim. The Name Elokim can be translated into other languages. But the Name Hashem is untranslatable. Because only a Jew can understand that Hakadosh Baruch Hu brings all of existence, past, present and future, into being. This is what the Name Hashem signifies.
The human being, as compared to the forces of nature, is a puny creature that is easily swept away by stormy waves of sea. The forces of nature act with tremendous power. A human being is small; he has no control over them. This is the reality of the world.
Hakadosh Baruch Hu created the world, and the world is full of dangers. There are sicknesses, threats to our parnassah, and so forth. Naturally speaking, you can’t get by in the world. You need Elokim, “G-d,” Who is above the forces of nature, Who has tremendous, awesome, supernatural powers. He holds the little human being by his hand and rescues him from the storms of this world.
This is why, in former times, every person in the world understood that he can’t get by in life without G-d holding him by the hand. (Nowadays, people don’t feel they need G-d anymore. They have a health plan, they have social security, they have the media, they have a microwave. Everything is taken care of...)
Avraham Avinu came along with a new idea: The One Who created all of reality it is also G-d! He is not just the originator of reality, He also stands next to us, with us. He takes care of us and understands us. He holds us by the hand and guides us along our way through a world fraught with danger.
This is what we are saying every time we recite a berachah. “Hashem,” the One who brings reality into existence, is “Elokeinu,” He watches over us and guides us on our path. And we emphasize that He is not just the G-d of the whole world; He specially watches over the Jewish people. He is “Elokeinu,” our G-d.
And the Name “Elokeinu” is in plural. This means that He is the G-d of each and every individual Jew, even of the one who refuses to recognize this.
If the Name “Elokeinu” would be in the singular, there would be room for some fool to come along and say, “Okay, He’s G-d, but He’s not my G-d. I am a sinner, an evil person. I transgressed all the mitzvos of the Torah and have severed all connection with Him.” This is why the Name “Elokeinu” is recited in the plural form. A person can close his eyes and try to ignore the tremendous treasure that is his, but it won’t help. As long as a person is a Jew, Hakadosh Baruch Hu is his G-d. And He watches over him specially.