Many modern English translations understand this phrase as a metonym for the success that his prudent behavior gave him, so they read, "had more success." (See: [[rc://en/ta/man/jit/figs-metonymy]])
Here "name" is a metonym for David. This can be stated in active form. Alternate translation: "so that people greatly respected David" (See: [[rc://en/ta/man/jit/figs-metonymy]] and [[rc://en/ta/man/jit/figs-activepassive]])