Yes but that predates and has nothing to do with the Act of Union. All the Act of Union did was to call the British and the Northern Irish part of something called the UK. It didn't bother to give a collective noun to the people. So that allowed for a variety of informal terms to come into circulation, the most common by far being 'British'. The only legal constitutional term to describe the political union between the two is the UK. [hl]So if people want to call themselves one or the other, that's their choice[/hl], but there isn't a 'right' answer because there isn't a legal term encoded in the founding document.