Why is the the Union Jack called the Union Jack?

There is some evidence to suggest that the name derives from the use of a small flag, flown from the small mast, mounted on the bowsprit. As at 1627 a small flag was commonly flown in this position

The correct name of the UK flag is the Union Flag and it represents the Union of England, Scotland and Ireland (Northern Ireland now). Strictly speaking, it should only be known as a 'Jack' when it is flown on a Royal Navy warship.