Names have meanings. Even if it is not your actual name, if you are called by it, it still has meaning. For instance, in the 1960s, if you had an encounter with “the mafia” and they brought in some guy called “Knuckles,” your heart would probably sink since he did not get that name for nothing.
In the same way, God calls Himself “Elohei-Yisrael”—“The God of Israel”—over 200 times in the Bible. Why? Perhaps He is trying to tell the world something about Himself. But what does He wish to say?
1) He is a covenant-keeping God. The Bible recounts God's covenant with Abraham, promising him a great nation (Genesis 12:1-3). This covenant was later reaffirmed with Isaac and Jacob, who were given the name Israel (Genesis 35:10). This signifies a special and permanent relationship between God and the people of Israel. BONUS: As a believer in Messiah, you too are grafted into that same family! He will keep His covenant with you through the Messiah. You can rest assured.
2) He gave them a job to do. I can call myself a policeman, but without a badge and authorization from the city, it is worthless. In the same way, the Israelites, as God's chosen people, were tasked with reflecting God's character to the gentile nations around them (Isaiah 42:6-7). His name, “The God of Israel,” backs up that calling. That name is their authorization, their badge, which shows the world they have a job to do. BONUS: As a believer in Messiah, you too have a job to do, to tell the gentiles around you about this same God. We call that “sharing our faith” or simply evangelism.
3) It shows the faithfulness of God: God's permanent relationship with Israel highlights his unwavering faithfulness to his promises, even when Israel sins. BONUS: Unless you are in glory, you too can still sin. But that should not mean God will abandon you at the first sin. His Spirit gently guides us back into the fold with repentance, as He did for Israel. This brings great comfort to anyone who fears falling too far. “I will never leave you nor forsake you.” (Hebrews 13:5)
While there are many more reasons God calls Himself “the God of Israel,” these three show us some deeply important things: 1) God keeps His covenant. 2) God calls us to work and witness for Him. 3) He doesn’t abandon us when we fail.