"North" or "Northern" as adjective [duplicate]

Solution 1:

It's largely (but not completely) arbitrary whether to use, say, North or Northern as a modifier.

In contexts where North X is a well-recognised "entity" (North Korea, North America, for example), there's a very strong tendency to use the shorter North.

In contexts where there's more the sense of an "ad-hoc" distinction being made between the geographically-distinct areas within "X", the tendency is to use the more overtly adjectival form. Thus we're likely to refer to "Northern Alpine slopes", or Northern England, because these areas are still fundamentally perceived as being part of "the Alpine slopes", or "England", rather than autonomous entities.

But as been mentioned in comments, in many cases (names of institutions, for example), it's entirely a matter for the people in charge what they call themselves. They may have reasons for their choice which have little or no relevance to how others see things.

Solution 2:

It is arbitrary. Typically somebody thinks which sounds best in a particular case and then others copy them. But as an adjective there is no rule.

South Africa is a country, part of the region of southern Africa: one of its provinces is called Western Cape, but could easily have been called West Cape and is in Afrikaans (Wes-Kaap).