Why is she known also Elizabeth the second when Elizabeth the first was only English? Surely the name Elizabeth II doesn't make sense after the Act of Union and in the Commonwealth?
The naming convention of Britain and later the UK was basically just inherited from England.
It's been changed so that whoever of England or Scotland has the greatest number from their respective thrones will be the monarch name. So for example if there is another James he will be James VII (inherited from Scotland), not James III.