He added: “I was looking for something like ‘James Dean’, I was looking for something short and sweet. I thought, well, I’ll keep the name Nicolas because my father [the late professor August Coppola] named me Nicolas – with French spelling, which has always frustrated me, because everyone adds an ‘h’. I don’t know why he gave me the French spelling! But he did.”
Article source: https://www.huffingtonpost.co.uk/entry/nicolas-cage-changes-name_uk_6a19aeb4e4b005ae41805a69