The correct term used to describe the process by which an outsider, immigrant, or subordinate group becomes indistinguishably integrated into the dominant host society is known as acculturation. This term refers to the process of adopting certain cultural aspects, beliefs, and values of the dominant group while retaining some aspects of their own culture.

Option 1: Accommodation refers to providing or adjusting something to meet the needs or wants of a specific individual or group. While accommodation can be a part of the acculturation process, it does not fully capture the concept.

Option 2: Cultural imperialism refers to the dominance or imposition of one culture over others, often through colonization or economic means. This does not accurately describe the process of integration.

Option 4: Adaptation refers to the process of adjusting or changing in response to new circumstances. While adaptation is often a part of acculturation, it is not synonymous with the complete process.

In summary, option 3, acculturation, is the most accurate term to describe the process of becoming indistinguishably integrated into the dominant host society while retaining some aspects of one`s own culture.