I'm guessing he would either have reigned as King Frederick (no ordinal number would be used until a second King Frederick occurred) or taken his father's name or the name of a previous British monarch.
As with his grandfather above, he would have reigned either as King Ernest or taken the name of a predecessor.
In the 20th century, three kings assumed regnal names in place of their given names ie. Albert Edward became Edward VII, David became Edward VIII, Albert became George VI so that may well have been the same tradition followed by those earlier examples.
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