Deed Poll Records

I was wondering if I received a unilateral act to change my name, would there be a new record in the register of births of myself with my new namea

No, you must change your birth certificate.

I'm not sure!

what the guy said above ^^^^^^

But I would change my name too
Glutius Maximus

No, it would not change a birth certificate. In general, you get a Deed Poll instead of changing your birth certificate.