You often cannot amend the name on your certificate of naturalisation and generally there is no need to.
In the UK, you can legally use your married name and there is no requirement to officially change you name. You can also get a passport in your married name. However it is important to note that HMPO will not issue a British passport in your married name
unless you also change your name in your current passport.
See:
https://www.gov.uk/changing-passport-in ... artnership
Advice is given based on my personal research and experience only. Do NOT contact me via private message for immigration advice