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all of Judah
Here "Judah" represents the people. AT: "all the people of Judah" (See: rc://en/ta/man/translate/figs-metonymy)
My name will no longer be called upon by the mouths of any of the men of Judah in all the land of Egypt
Here "name" represents the whole being of Yahweh. And, "mouth" represents the whole person. This can be stated in active form. AT: "No person of Judah living in the land of Egypt will ever call upon me again" (See: rc://en/ta/man/translate/figs-metonymy and rc://en/ta/man/translate/figs-synecdoche and rc://en/ta/man/translate/figs-activepassive)
As the Lord Yahweh lives
"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. AT: "I solemnly swear" or "I solemnly swear by the Lord Yahweh" (See: rc://en/ta/man/translate/figs-idiom)