Well Terpe, in that case, sorry but you are completely wrong.
I am extremely aware of the UK law on changing one’s name.
I was the o/i/c of the passport section of The Met Police for a while and had close liaison with the Registrar General’s office, Birth, Deaths and Marriages, of the UK . It was whilst I in that post that I changed my name.
I subsequently changed my name on all my paperwork, except as I said, on my Birth Certificate.