Under the background of China's "One Belt One Road" initiative, the cultural differences between the Chinese and western languages should be considered in the going-out of the Chinese enterprises and the coming-in of the foreign ones. This paper studies brand extension naming strategy with the methods of case study and experiment from the perspectives of market and consumers. It selects China and the U.S. as the representatives of the collectivism and individualism cultural framework. It finds that the differences in the brand extension naming are consistent with those in the naming of people. Consumers from the collectivism cultural background prefer the relational naming strategy of stressing the parent brand and family while the consumers from the individualism culture favor the personalized naming strategy of stressing sub brands and independence. This paper tries to explore the preferences of brand extension naming strategies under different cultural backgrounds, providing the theoretical basis for companies in the cross-cultural market to adopt the appropriate brand extension strategies.