If a person's name makes that person distinguishable from a typical American, then that person's name shows that the person is not assimilated into the American culture.
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Cultural assimilation is the process by which a person or a group's language and/or culture come to resemble those of another group. The term is used to refer to both individuals and groups, and in the latter case it can refer to either immigrant diasporas or native residents that come to be culturally dominated by another society. Assimilation may involve either a quick or gradual change depending on circumstances of the group.
Full assimilation occurs when new members of a society become indistinguishable from members of the other group. Whether or not it is desirable for an immigrant group to assimilate is often disputed by both members of the group and those of the dominant society.
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If you want to be employed by an employer that is from a culture different than the one you are from, you must show a willingness to be assimilated into that culture or show that you can be integrated with that culture.
If your name shows you reject that other culture, then expect that the people hiring think you want separation or marginalization, and would not be a good fit for the culture of their organization.
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Acculturation
The fourfold model categorizes acculturation strategies along two dimensions. The first dimension concerns the retention or rejection of an individual's minority or native culture (i.e. "Is it considered to be of value to maintain one's identity and characteristics?"). The second dimension concerns the adoption or rejection of the dominant group or host culture ("Is it considered to be of value to maintain relationships with the larger society?") From this, four acculturation strategies emerge.
Assimilation occurs when individuals adopt the cultural norms of a dominant or host culture, over their original culture.
Separation occurs when individuals reject the dominant or host culture in favor of preserving their culture of origin. Separation is often facilitated by immigration to ethnic enclaves.
Integration occurs when individuals are able to adopt the cultural norms of the dominant or host culture while maintaining their culture of origin. Integration leads to, and is often synonymous with biculturalism.
Marginalization occurs when individuals reject both their culture of origin and the dominant host culture.
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You are being too narrow in your suppositions.
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Americanization is the process of an immigrant to the United States of America becoming a person who shares American values, beliefs and customs and is assimilated into American society. This process typically involves learning English and adjusting to American culture, and customs, while keeping the old foods and religion. The ethnic groups undergoing Americanization not only retained their traditional cuisines, but they also spread to the wider American public for their taste of pizza, bagels and tacos.
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