Here the word "name" represents Yahweh's reputation. Alternate translation: "for the sake of my reputation" (See: [[rc://en/ta/man/translate/figs-metonymy]])
This can be stated in active form. Alternate translation: "so that the people would not profane it in the eyes of the nations" (See: [[rc://en/ta/man/translate/figs-activepassive]])
The eyes represent seeing, and seeing represents thoughts or judgment. Alternate translation: "in the opinion" or "in the judgment" (See: [[rc://en/ta/man/translate/figs-metaphor]])
The word "nations" is a metonym for the people who live in the nations. Alternate translation: "the people who live in other nations" (See: [[rc://en/ta/man/translate/figs-metonymy]])
Here the word "them" refers to the nations. The idiom "in their eyes" refers to being in a position where people can see. Alternate translation: "I revealed myself to them, in their presence" (See: [[rc://en/ta/man/translate/figs-idiom]])