A narrative that stresses Hitler's unveiling of the KdF-Wagen in 1938 to the Beetle of the counterculture thirty years later leaves out an important middle period in this car's history. This interregnum, lasting from the late 1940s to the 1950s was quite essential for Volkswagen to rebrand both the company itself and its products for the global market.

VW's prospects for survival did not look good in the immediate postwar period. The British occupation made plans for shipping the tooling for VW's Kubelwagen, the wartime version of the KdF-Wagen, to the UK, but no British car manufacturer was interested in them. Nor were the Americans much interested in the KdF-Wagen. The New York Times reported on the car in 1938, calling it "Baby Hitler," and ridiculed its small design. The company's survival hinged on a number of factors. Firstly, returning the company to a functional basis would ease unemployment in Wolfsburg area. In light of the emerging Cold War, both the British and the American occupation officials saw economic reconstruction as a proactive measure to prevent the Western zone from slipping into Communism. VW production also eased British occupation costs as it allowed the British forces to rely upon a vehicle produced in their occupation zone. On a more cynical level, some British officials felt that allowing VW to produce cars for domestic use and to export cars to Switzerland and Sweden would prevent American car companies from gaining a foothold while the UK auto industry made the transition to a peacetime economy.

The Western Allies scaling back of the denazification of industry suited all of these imperatives. The Joint Chiefs of Staff policy directive (JCS 1067) of May 1945 had called for an extensive reform and house-cleaning of German industry, but by 1947/48, officials in both the American and British zone had begun to backpedal on this commitment. German industrialists played an important role in the gutting of JCS 1067 as they launched a determined public relations campaign both in the Western zone and abroad portraying them as honorable and paternalistic capitalists whose patriotism made them victims of Hitler's cynical politics. In the case of VW, Ferdinand Porsche Jr., provided documents that allegedly proved that Hitler actively lied to his father by promising that the KdF-Wagen was to be used purely for peaceful means. VW's public relations campaign would contend that the use of slave labor and its other associations with the crimes of the Third Reich were not their responsibility, but rather foisted upon them by a criminal regime. Implicit within this denial of culpability was a counter-narrative that German engineering genius and responsible corporate management was a constant throughout the war and was now able to find full expression now that Hitler's criminal regime had been removed.

Many sarcastic wits in the FRG called this type of exculpatory memory Persilschein, after a popular laundry slogan in which "the Brown/stain washed out," meaning that claims to be denazified were cosmetic and more rhetoric than reality. However, the self-serving image of German companies like VW did strike a chord with consumers in the FRG in the first decades of the Wirtschaftswunder. One of the strongest early customers of the VW Beetle were German veterans and the VW capitalized upon their wartime experience with the Kubelwagen. Company materials and FRG public intellectuals celebrated the Kubelwagen's dependability in such diverse climates as Tunisia or Stalingrad, an association enabled by the notion of a "clean" Wehrmacht that was not responsible for the war crimes of the Third Reich.

But more important to the success of VW in the FRG than a sanitized wartime memory was that the company actively portrayed the Beetle as emblematic of the new Germany of the Wirtschaftswunder. The Beetle was a dependable, unassuming, and symbol of a resurgent economy. Compared to the hyper-politicized consumer consumption of the Third Reich, contrasted strongly with the avowedly unideological nature of the postwar Beetle. Whereas purchasing the KdF-Wagen was through the state, the new VW came through private means and German consumers could personally customize the vehicle to suit their needs. In the latter case, this was an important consumerist shift as purchasing the KdF-Wagen was not about individual choice, but being a part of the national community. The vehicle's small size and modest, but ever improving, features, which VW's advertising constantly trumpeted, stood in for the public image of Germany many West Germans sought to present to the world. VW became a symbol that the bombastic Third Reich had been transcended and replaced by a responsible member of the international community whose success was enabled by allegedly traditional German values like thrift and sobriety.

Celebrating the modesty of the Beetle also carried with it an implicit critique of American hypercapitalism and privileging of style over substance. This helped VW penetrate and expand sales into Western European markets like Scandinavia and the Low Countries. Although protectionism prevented VW from making inroads in countries with their own established auto industries like France, Itally, and the UK, the Beetle found many buyers in countries without a domestic auto industry like Denmark. VW would emphasize its products affordability, dependability, and small size. This experience with these tertiary markets helped VW to make the big leap over into the US and the global market in the late 1950s and early 1960s.

Helmut Krone's famous advertising campaign for VW certainly helped the Beetle to gain public recognition inside the US. Krone's advertisements were often humorous and thumbed its nose at Detroit's advertising norms. For example, Krone's department created large ads with minimal text and pictures and urged consumers to "think small." This helped cement the Beetle as a individualistic car that was counter to the conformist norms of American automobiles of this era (e.g. more horsepower, more tailfins, etc.). For the emerging counter-culture, the apparent anti-consumerist symbolism of the VW made it an attractive choice. But the success of the Beetle was not just due to an advertising campaign that built itself on German advertising norms. In short, VW had produced a type of vehicle that Detroit was not interested in producing. The Beetle was cheap and more or less reliable, making it an ideal second car or one for poorer consumers. The inroads the Beetle made in America were not as alarming to Detroit and other American commentators as the success of Japanese cars in the 1970s. For one thing, VW was serving a market share that Detroit had largely ignored such as women, and because of the relatively buoyant American economy, this did not seem as much of a threat. For the American press, signs of the VW's success was a sanctification of America's leadership during the Cold War. That VW had recovered and produced a product that now had a global market was a sign that America's tutelage was more valuable than the Soviet Union's Marxist-Leninism. VW's public relations campaign that they were responsible capitalists meshed well with this triumphalist idea of American leadership.

Of course, the VW's Third Reich heritage was an open secret. Even during the early days of the postwar Beetle, there were many jokes about its connection to the Third Reich such as "how many Jews can fit into a Beetle?" (hint, the punchline involves an ashtray). William Manchester's bestselling 1968 polemic The Arms of Krupp exposed a lot of German industry's dealings with Hitler and its self-serving postwar campaign to distance themselves from their relationship with the Third Reich. The press in the GDR frequently mocked the pretensions that the FRG had made a decisive break with the prior regime and reveled in exposes drawing lines of continuity between the Third Reich and the FRG's industrial and governmental. Many of these critiques would be picked up in the FRG's New Left intellectuals who targeted the hypocrisy of West German industrial firms like VW. While VW steadfastly maintained it was a responsible corporate entity, it was adamant in refusing compensation for wartime forced labor well into the 1990s.

But explicitly connecting the Beetle to the Third Reich was largely restricted to cultural outliers in the postwar era. The Beetle filled important niches in the automotive market that dovetailed with German industry's attempt to cleanse itself of any connection with the Third Reich. In the US, the strong economy meant the Beetle was a curiosity, not a threat to a major industry or America's geopolitical standing. So there was little impetus in bringing up either the vehicle's or the company's Axis past, unlike in the 1970s. By shrewd marketing and an economic and political context that promoted selective amnesia about the past, VW managed to disassociate itself from its origins as Hitler's car.

Sources

Hiott, Andrea. Thinking Small: The Long, Strange Trip of the Volkswagen Beetle. New York: Ballantine Books, 2012.

Rieger, Bernhard. The People's Car: A Global History of the Volkswagen Beetle. Cambridge, Mass: Harvard University Press, 2013.

Wiesen, S. Jonathan. West German Industry and the Challenge of the Nazi Past, 1945-1955. Chapel Hill, NC: University of North Carolina Press, 2001.

Volkswagens were somewhat successful in the 1950s, in Western Europe. In the US, the Volkswagen was seen as to small, to slow and to weird to be more than a niche car. That all changed when Helmut Krone became the art director for the Volkswagen account at VW's advertising agency.
Krone's advertising under sold the car, with self deprecating and some what humorous television commercials. In 1999, Advertising Age, a leading Industry journal, proclaimed Krone's 1960-1965 Volkswagen ads to be the best advertising campaign of the twentieth century. In the third episode of Mad Men's first season, Don Draper and his co-workers were dissecting one of Krone's ads. While Draper did not like it, it was one of the few actual early 1960s advertising that resonated enough, to be critiqued, fifty years later, on Mad Men.
Source: "Helmut Krone" by Clive Challis

To piggyback on this question, can anyone elaborate on how companies generally transitioned in post Nazi Germany?