Possible meanings are 1) she wrote Ahab's name on the letters. Alternate translation: "wrote letters and signed them with Ahab's name" or 2) the word "name" is a metonym for authority. Alternate translation: "wrote letters on behalf of Ahab" (See: [[rc://en/ta/man/jit/figs-metonymy]])
The word "wealthy" refers to wealthy people. Alternate translation: "the wealthy people who sat with Naboth" (See: [[rc://en/ta/man/jit/figs-nominaladj]])