As immigrant arrivals to the united states peaked in the mid-1900s, the broad array of new arrivals dispersed into cities and towns, often blending in to both embrace their new lives and as a way of being safe against prejudice and hatred. this process has often been called

The process has often been called Americanization.

Explanation:

Americanization is a specialized concept that includes the assumptions of the Melting Pot Theory that stands that when two cultures meet there is a process called Cultural Assimilation in which the minority group tend to adopt cultural characteristics such as language, behavior, traditions, and so on, until they melt. It could happen that the minority group blend so much that end up identifying as the dominant culture, or it could happen that the minority group still have characteristics of their mother culture but mixed with the new one. Both cases are cultural assimilation in the Melting Pot Theory.

United States since the end of the 1800s had an increased number of foreigns, later increased even more with the Great War mostly (also when Alaska was purchased from Russia, there was indigenous groups that needed to assimilate US culture). So the government started a movement with programs to teach english and civil laws to foreigns, also to help them adapt and establish legally in the country in the case of immigrants. This is a cultural assimilation movement called Americanization.

As the question is pointing out a cultural assimilation of immigrants but particularly those that arrived to United States the correct answer of the process is Americanization.