The share registry, MUFG Pension & Market Services (formerly Link Market Services), is responsible for the administration of your holdings, so you will need to contact them directly.
It'll often require a form to be completed and sent to them. You may need to provide certified ID.
MUFG Pension & Market Services have a handy FAQ where they cover this under Updating your Details > How do I change my name?
You can also find their forms here.