It is not necessary for British citizens resident in Ireland to register with the Embassy, however if you wish you can register with the Foreign and Commonwealth Office on http://www.fco.gov.uk/en/travelling-and-living-overseas/Locate/

As there is no Consular Agreement between the United Kingdom & Ireland the British Embassy does not register the births, marriages or deaths of British Nationals abroad.

If you are resident in Ireland,  enquiries regarding naturalisation and registration as a British citizen through either residency in the UK or marriage to a British citizen should be directed to our Consular Section