This type of marking was not unique to either the V-2 or the Saturn V. Test versions of rockets have often had black and white markings to help engineers analyze their flight characteristics. As mentioned in this answer this was true also of the prototype V-2 rockets. While many people associate the V-2 with the checkerboard pattern typically seen in photos, operational V-2 rockets had a completely different paint scheme. As mentioned in the Wikipedia article about the V-2:
During tests the rocket was painted in a characteristic black-and-white chessboard pattern, which aided in determining if the rocket was spinning around its longitudinal axis .... The painting of the operational V-2s was mostly a ragged-edged pattern with several variations .... at the end of the war a plain olive green rocket was also used.

Operational V-2s (National Museum of the United States Air Force, both photos)
In 1945 as WWII neared its end, Wernher von Braun and several other German scientists surrendered to the Americans. After the war was over they provided assistance in the U.S. rocket program, with both von Braun and Kurt Debus reaching high level positions. After test launching several captured V-2s in
New Mexico, an improved U.S. version was created, the PGM Redstone which had tracking markings, but not the same markings as the V-2.

PGM-11 Redstone first launch August 20, 1953 (U.S. Army)
Redstone rockets with similar tracking markings were flown over the next several years for scientific and nuclear test launches. However the Army tactical versions were painted solid colors.

Army Redstone missile 1960 (Wikimedia Commons)
A nearly identical situation existed in Russia after WWII, as Sergei Korolev and his team built a Russian copy of the V-2 named the R-1. Sometimes referred to as P-1, R is a transliteration of the Russian “P” in paketa (raketa, or rocket). Notably the Soviet (i.e. non-von Braun) R-1 also had black and white markings.

Soviet R-1 1946 (S.P.Korolev RSC Energia, via Wayback Machine)
The Soviets then designed an improved version, the R-2.

Soviet R-2 (Ministry of Defense of the Russian Federation, via Wikimedia Commons)
The British painted their test V-2s in the original checkered paint scheme when they cobbled together what was essentially leftover V-2 parts after the war, during Operation Backfire.

Operation Backfire V-2 launch (Science Museum UK, via Wikimedia Commons)
I didn’t find any photos of R-7 family test rockets for Sputnik, Vostok, and Soyuz with these type of markings, presumably the side boosters provided roll tracking capability. A similar situation existed with the Space Shuttle which also did not have tracking markings since the wings and side boosters made it possible to track roll. As a side note the three British Concorde prototypes, which were developed in the same general era as the Saturn V, had various checkerboard markings on their fuselage.

Concorde development aircraft G-BDDG
In the late 1950's it wasn’t just the Army Redstone program working towards orbital flight, there was also the Navy Vanguard program (which Wernher von Braun had nothing to do with), which also had black and white markings for tracking.

Vanguard carrying Vanguard 1, 1958 (NASA)
For geopolitical reasons Vanguard was initially given the task to put America’s first satellite into orbit instead of the Army Redstone. However after the Soviets launched Sputnik in 1957 this task was shifted to von Braun’s Juno Redstone derivative, which launched Explorer 1 in January 1958, with the Juno having similar tracking markings as Redstone.

Juno I carrying Explorer 1, 1958 (NASA)
Vanguard did however put the second U.S. satellite Vanguard 1 into orbit in March 1958.
As mentioned in the other answer, Mercury-Redstone had black and white tracking markings

Mercury-Redstone 3 carrying Alan Shepard, May 1961 (NASA)
as did the (non-Wernher von Braun) Titan II

Gemini-Titan II carrying Pete Conrad and Dick Gordon, September 1966 (NASA)
The other crew-rated Saturn rocket, the Saturn IB, made the final flight in the Saturn program in 1975, five years after Werner von Braun had left the Saturn program for an administrative role in NASA.

Saturn_IB carrying Tom Stafford, Vance Brand, and Deke Slayton, July 1975 (NASA)