Yes and no. It's the term for the west coast, but not really a proper name. Capitalising such geographical terms in native language but not in translation is reasonably common. And the American West Coast is translated as den amerikanska västkusten in Swedish, so that's the exact same thing there.
Consider how English "at" can mean either "on" or "by" - Swedish uses på for the "on" meaning of "at", and vid for the "by" meaning.
That's generally speaking, though... there's not exactly a rule that applies to everything, since the prepositions are so common.