I can't say for sure, but I think CPH as airport code comes from the common abbreviation for the city, rather than the other way around. KBH (København) is also

I can't say for sure, but I think CPH as airport code comes from the common abbreviation for the city, rather than the other way around. KBH (København) is also used in Danish fairly commonly, and isn't any airport's code. It's possible that KBH is a backformation from CPH, though, come to think of it. Might try to dig into that if I have some spare time.