Not 'the city of York'.
York St John University
Unless space is very limited, always use 'York St John University' in full, even in subsequent mentions on the same page. If you have named the University once on the page, we recommend switching to use 'us' or 'we' for subsequent references. If a reduced version must be used, use 'York St John' or 'YSJ', not 'YSJU'.
Not 'YSJ Active' or 'YSJactive'.