England was called England. England did not become a part of Normandy. The Duke of Normandy assumed the position of King of England. As soon as William the Conqueror died the two positions were separated again for a while, until Henry I invaded Normandy and put out his brother's (the Duke's) eyes. Also, in geographical terms, "England" referred to the area England now occupies and nowhere else. Scotland, Wales and Ireland were most definitely not part of "England". The only areas of variation would have been the Welsh and Scottish marches.
Although England was ruled by a bunch of people we now refer to as Normans, the only people who generally called them Normans at that stage were the Normans. To the English they were "Franks" and to the French anyone who came from England was "English".
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