When an individual provides personal information to an organisation, they are not giving it away. That organisation doesn't own it, control it or have full rights to it. An individuals personal information cannot be treated like a patent of copyright. They have the right to request from any organisation without undue delay or question, changes to their data.
Most computer systems track historical changes to data. This leads to the possibility that an organisation can capture all changes made regarding sex, gender, preferred name and title. Its important that if this happens customers are made aware of this and given the option of having this data erased. Such information has no business or legal benefit to the organisation and can only result in its misuse if its kept.
In the case of maintaining an audit trail regarding the legal name of an individual, this is allowed provided the customer is informed. The requirement to maintain a historical trail of legal names of an individual might be required by an organisation for legal reasons and is to be handled separately.