This would be an odd one. The last king of this name reigned as James II of England and VII of Scotland, keeping separate ordinals for each of his kingdoms. His displaced son adopted the title of James III and VIII whilst in exile. A new king of this name calling himself James VIII might be confusing for his English subjects, the vast majority, who have only known two earlier kings of this name.
Of course a new king of this name should really be styled James I of the United Kingdom but that might prove just as confusing.
Choosing ordinals can be a tricky business.