The early prototypes of the A4/V2 were painted in the familiar
black-and-white roll pattern scheme. This scheme was designed to aid
in tracking the rocket after launch. This pattern made it easy to
observe any variation or roll of the rocket. The exact pattern was
changed many times, and as with the rest of the rocket, the pattern
was examined and altered if warranted.
Camouflage colors were introduced to the A4/V2 during the middle of
1943. At the beginning, three different schemes were designated to be tested;
But the Saturn V was a very different rocket, three instead of one stage and very huge. The height of a V-2 was 14 m, much shorter than the third stage of Saturn V alone with 18.8 m.
Visual and film camera observation was used too, so a black-and-white roll pattern scheme was used. But only a small lower and upper part of each stage was colored with black and white stripes and the large parts in white only to reduce heating by sunlight.
Image from www.bernd-leitenberger.de.
A similar coloring scheme was used for the Mercury-Redstone Launch Vehicle and the Gemini-Titan II rocket.
But von Braun was not the only one German rocket scientist working on both V-2 and Saturn V. There were hundreds of scientists working on both rockets, so the design of the color pattern could be done by somebody else. See Operation Paperclip.