If an organisation has identified the need to store the legal name of an individual, then they have the right to request legal documentation showing any change in name. An individual will need to produce this documentation to have their legal name changed.
For a preferred name, this is not subject to legal constraints and a customer on request of a name change is not required to produce any documentation proving that change of name.
This is why it is important organisations distinguish between the legal name and the preferred name.
Employers can request the legal name for the purpose of establishing a contract with their employee. Even so a contract can be made and is still binding using preferred name when signed.