"GBP" is a written convention used in exchange markets and a few other places. We don't "say" GBP.
GBP does not stand for "Great Britain pounds" or "Great British pounds", and neither of those phrases is correct or idiomatic. The currency is referred to as "the pound", "the British pound", or "the pound sterling".
The ISO 4217 currency code is GBP, formed from "GB", the ISO 3166-1 alpha-2 code for the United Kingdom, and the first letter of "pound". It does not stand for "Great Britain Pound" or "Great British Pound". Occasionally, the abbreviation "UKP" is used but this is non-standard because the ISO 3166 country code for the United Kingdom is GB
UK v GB
"UK" is normally the abbreviation for "United Kingdom", but as Wikipedia observes, "GB" is the ISO code for the United Kingdom. It is also used as the international vehicle registration code. It is actually the UK's country domain (.uk) that is the odd one out in terms of international codes, although:
.gb is a reserved Internet country code top-level domain (ccTLD) for the United Kingdom.
UK / Britain / Great Britain
My assumption would be that the term GBP was coined before NI became a member of the UK in 1922
I don't know when it was coined, but before 1922 the inaccuracy would have been even greater, since the country was then the United Kingdom of Great Britain and Ireland, i.e. the whole of Ireland was part of the UK.
Of course, many writers over the centuries have treated "UK", "Britain" and "Great Britain" as synonyms (the same is traditionally true of "England" to a large extent - George Orwell regularly used "England" to mean the UK, and Shakespeare referred to England as an "isle"; this usage of "England" is no longer considered acceptable in the UK, but remains widespread fairly outside the UK). Today, the term "British" is still widely used to mean "of the UK" (including by the UK government, e.g. https://www.gov.uk/world/embassies ; https://www.gov.uk/becoming-a-british-citizen ), and "Britain" is often used to refer to the whole UK ( http://www.nationalarchives.gov.uk/cabinetpapers/themes/korea-entry-britain-war.htm ). These usages of "Britain" and "British" are generally considered acceptable. "Great Britain" is more likely to be reserved for geographically accurate usage, although not always (especially in older works).