If there's NO magnetic field piercing a surface (inward or outward),
then it is not a pole at all.
If Magnetic field comes outward through some surface,
we could call that surface a North pole ... (or it is NEAR a North pole).
Most precisely, that surface area has "positive magnetic flux" outward.
The opposite is for magnetic field piercing INto a surface ...
call it a South Pole, or surrface Area with negative magnetic flux.
As a definition ... why does this bother you?