Changing your name in Northern Ireland by deed poll follows the same fundamental principle as in England and Wales: you sign a document declaring your old name and your new name in front of two adult witnesses, and from that moment it is your legal evidence of the change. The major UK-wide organisations (the Passport Office, DVLA, most banks, HMRC, and your GP) all accept a deed poll from a Northern Ireland resident in exactly the same way as one from England or Wales.
Northern Ireland has its own legal system, and historically a sworn deed poll (executed as a deed and sometimes called an enrolled deed poll) was more common there than the simpler unenrolled form. In practice, for everyday name changes with the organisations most people deal with, an unenrolled deed poll produced by this service is widely accepted. If you need a deed poll for a specific legal purpose (amending records with the General Register Office for Northern Ireland, or use in proceedings), a solicitor in Northern Ireland can advise on whether a more formal process is required.
For birth certificate amendments in Northern Ireland, a deed poll alone is not sufficient. Birth certificates in Northern Ireland are managed by the General Register Office for Northern Ireland. Changes to a birth entry require specific processes that go beyond a deed poll. For all other day-to-day purposes (passport, driving licence, bank, employer, National Insurance), a deed poll is the right document.