A Statutory Declaration was required to modify facts as a marginal annotation with the original entry preserved. Re-registration under Legitimacy Act (NI) 1928 or Ireland (1931) created an additional new entry.
Dublin GRO continued to be copied with changes in Belfast after partition for births that occurred pre-partition so official paper certificates issued from either location/juristiction would contain the same info. Have seen several, below is one.
https://irishgenealogy.ie/files/civil/birth_returns/births_1910/01563/1631013.pdfEntry #440 for a 1910 birth in Belfast with surname corrected from Porter to Porte in 1939 by S.D. by the mother who was the original informant.
Others where original informant has died may say something along the lines of by XX who was aware of the true facts of the matter, or your Newbridge one the S.D was by an elder brother 'present at the birth', wonder what age he was in 1887.