Final answer:
The government policy that sought to destroy Native American culture and assimilate them into Euro-American society was known as Americanization, involving the creation of boarding schools and altering land ownership practices.
Step-by-step explanation:
The name of the government policy that aimed to destroy Native American culture and assimilate Native Americans into Euro-American society was known as Americanization. This policy included efforts such as removing Native American children from their families and placing them in boarding schools, like the Carlisle Indian School, where they were forced to abandon their language, clothing, and traditions in favor of Euro-American customs. These schools provided vocational and domestic science training, and the broader policy saw the transfer of surplus tribal lands to settlers under the guise of land allotment. The policy not only aimed to integrate Native Americans into the dominant culture but also frequently resulted in trauma for Native students and economic hardship for Native populations.
By the 1950s, additional policies such as Termination aimed to end special programs and federal recognition for Native Americans, pushing for their 'rapid and complete assimilation' into mainstream American society. This policy was met with opposition and was eventually deemed a failure, leading to a shift in focus towards strengthening Native American self-governance and cultural revival.