How should a father act after his ex-wife changed his daughter's first name and family name? Is he still obligated to financially support her after she disassociated herself from his family name? And how should he act if the mother does not respond to returning the daughter's lineage to her real family?

A person's attribution to other than his father is a great abomination. The woman and her daughter must be advised to repent to Allah and to restore the girl's name to its correct form. If it is possible to change this abomination through legal means, then let it be done. The daughter's maintenance is obligatory upon her father, unless she possesses wealth. Her actions or her mother's actions in committing this forbidden act do not waive the maintenance.