Here "name" represents the whole being of Yahweh. And, "mouth" represents the whole person. This can be stated in active form. Alternate translation: "No person of Judah living in the land of Egypt will ever call upon me again" (See: [[rc://en/ta/man/jit/figs-metonymy]] and [[rc://en/ta/man/jit/figs-synecdoche]] and [[rc://en/ta/man/jit/figs-activepassive]])
"as surely as the Lord Yahweh is alive." The people use this expression to show that what they say next is certainly true. This is a way of making a solemn promise. See how you transited "As Yahweh lives" [Jeremiah 4:2](../04/02.md). Alternate translation: "I solemnly swear" or "I solemnly swear by the Lord Yahweh" (See: [[rc://en/ta/man/jit/figs-idiom]])