Is it permissible to change the father's name in official documents—while preserving the family name—to facilitate obtaining employment, avoid racial discrimination, and reduce the length of the four-part name in official documents?

The question is not clear enough. However, if the intent is to change the name to match the father's name, such as the son's name becoming "Abdullah" and his father's name also being "Abdullah," then there is no objection to that in principle, as long as it does not lead to lying, cheating, or the invalidation of a right, and provided that the father's name is not forbidden by Islamic law. Such instances were found among the Companions and those who came after them.