Paschal Donohoe (Dublin Central, Fine Gael) | Oireachtas source

I will read out the note on this while I ponder the answer to the question. The Birth Information and Tracing Act 2022, which was signed into law in June, amended the Succession Act 1965 to make provision for persons who have been the subject of incorrect birth registrations.

The amendments provide that a person affected by an incorrect birth registration, who is referred to in the legislation as an “affected person”, will, in addition to his or her existing right of succession in relation to his or her birth parents, have succession rights in relation to his or her “social” parents, that is, the people he or she grew up understanding to be his or her parents.

That means that while you cannot change who your birth parents are, you can make a decision to select "social parents" and they will benefit from the terms of the Succession Act.