Cross Gates was reliably recorded in 1771. An earlier spelling "Crosyate" was used as far back as 1481. So the placename was in use long before mining came to the area.
The English placename society used to think that the cross gates were actual gates but that view has been superseded by the cross roads interpretation.
I don't have any special knowledge on this so I bow to their authority( and my old junior school teacher who taught us about the Vikings
)