Emmanuel (also spelled Immanuel) is a Hebrew name that means "God with us." It comes from two Hebrew words: El, meaning "God," and immanu, meaning "with us." The name appears in Isaiah 7:14, where the prophet Isaiah declares: "Therefore the Lord himself will give you a sign: The virgin will conceive and give birth to a son, and will call him Immanuel."
This prophecy is quoted in the New Testament in Matthew 1:22-23, where the angel explains the significance of Jesus' birth: "All this took place to fulfill what the Lord had said through the prophet: 'The virgin will conceive and give birth to a son, and they will call him Immanuel' (which means 'God with us')." The name expresses the central Christian belief that in Jesus, God became incarnate and dwelt among humanity.
The other options do not correctly translate the name. "God of Israel" is a title used for God but is not the meaning of Emmanuel. "God our refuge" translates a concept found in Psalms (e.g., Psalm 46:1) but not this name. "God saves" is the meaning of the name Jesus (from the Hebrew Yeshua), not Emmanuel.