Why is the queen of England called the II if elizabeth I had no children?

Answer 1

Because she is the second queen to rule England of that name.

It has nothing to do with having children, or else William I, Richard I, Richard II, Edward VI, Mary I, Charles II, William III, Mary II, William IV and Edward VI would also not count for none ever had a legitimate child.

If you only count the ancestors of the current queen even less would count, since some had children, but they or their lines died out, like Henry IV, Henry V, Henry VI, Richard III, Anne and George IV.

Answer 2

It is not like a father Robert naming his son Robert Jr. Elizabeth I had no children and the Elizabeth II only means she is the second queen named Elizabeth.