What is the ruling on a Muslim in the West changing his Arabic name to a foreign name, such as changing names like Ali, Omar, and Mahmoud, to avoid racial discrimination or assault, knowing that the change is formal and not in belief?

There is no harm in wearing a cross if there is a genuine necessity for it, and the motive is not to imitate disbelievers, provided that it does not carry a meaning forbidden by Islamic law, such as being a specific symbol for non-Muslims, or involving worship of other than Allah, or self-praise.