To adapt to the culture of your new home is known as: brainwashing. Americanization. assimilation. urbanization.

This is assimilation!

Americanisation means to make something more American, but this can also happen if you are not in fact in America, as in: America is not your home.

Urbanisation is the mass movement from the rural areas to urban areas.

Brainwashing is when someone uses extreme techniques to influence other's opinions. (such as psychological manipulation)