Ask for a mark, not a picture. The phrase that changes everything is “flat vector logo mark, centered on a plain white background” — it drops the model out of illustration mode into design mode: one idea, flat fills, clean silhouette, no scenery. A structure that works nearly every time is: “[style] logo mark of [one concrete object], [construction detail], flat vector, [two-color palette], plain white background, no text”. Style words carry real meaning here — monoline, geometric, emblem, negative space, gradient app icon and hand-drawn all produce genuinely different construction, not just different decoration.
Leave the company name out of the prompt. Small lettering is where image models still break down, and a garbled wordmark ruins an otherwise good symbol — generate the mark, then set the type yourself in Figma or Illustrator, which is how the pairing is designed in real studios anyway. Every mark below is the unedited first output of its prompt on BananaBanana; at $0.03 per Lite image you can explore forty directions for the price of a coffee before committing to one.