Covering the upper half of the convex lens with black paper reduces the amount of light that passes through the lens. While the entire image will still be formed, it will be dimmer because less light is refracted to form the image. The size and position of the image will remain the same, albeit with less intensity.
Every part of a convex lens contributes to the formation of the image. Blocking part of the lens does not block part of the image; it just reduces the overall amount of light contributing to the image formation, making the resulting image fainter.