Yahweh destroying David's enemies is spoken of as if Yahweh cut them off, as one would cut a piece of cloth or cut a branch from a tree. (See: [[rc://en/ta/man/jit/figs-metaphor]])
Here "name" represents a person's reputation. Alternate translation: "I will make your name to be great and well known" (See: [[rc://en/ta/man/jit/figs-metonymy]])