The answer is yes, you can change the surname without the fathers knowledge or permission. But at the age of 19 that wouldn't be an issue anyway. As long as it is done through a solicitor and you get the relevant paperwork saying that the 'old' surname will no longer be used all of the future documents (passport, licence etc) will be in the new surname.
I changed my sons surname, many years ago now. The first time I applied for a passport for him and his driving licence (years later) you have to send the original birth certificate with the deed poll letter and the docs will come back in the new name.
It's bit of pain the first time things are applied for but much easier when they need renewing.
HTH