"pretty much the same" so there will be a change? Negotiated with the EU or what?
And the name thing has been debated ad nauseum but the fact remains per Article 1 that the new country would be "United as one Kingdom called Great Britain" and article 2 refers to " .. the United Kingdom of Great Britain".
The fact remains that two Kingdoms were united into one. Without Scotland or England being United there would have been no United Kingdom of Great Britain for Ireland to join.