Q. if a woman loves her husband and the husband loves his wife. Can they exchange last names?

A. If the husband has a father, then he cannot attribute another persons last name to himself. This is forbidden. Also to attribute another persons linage as your own is linked to deception. Deception in Islam is forbidden.

A woman need not change her last name, if they both agree to keep their own last names.

Allah Certainly Knows Best.