Why do airlines name themselves for example "Cathay Pacific" or "Virgin Atlantic". Aren't they indirectly limiting themselves to always fly over "Pacific" or "Atlantic"? It would be weird if Virgin Atlantic flies over Pacific and vice versa.
In a lot of cases it's because they started serving a specific region.
Lucky tells the story of Cathay Pacific. Virgin Atlantic was started specifically to fly from Britain across the Atlantic. Lots of US airlines started in a specific region, like Southwest. Westjet started serving the west of Canada.
It doesn't make sense to change a well-known name just because the reach of the airline is extended.
The naming of an airline completely left to the investor(founder) who is registering the airline name. Reason behind the naming for the one you are referring "Cathy Pacific" is Cathay, the ancient name given to China and Pacific because Roy Farrell (one of the founding member of airline) speculated that they would one day fly across the Pacific. More on this can be found here.
There may be a reason behind the name or may not be. I feel that it is not necessary to have a particular reason behind the airline naming or even other naming convention.
The name of a business is the business's brand name so people can identify it easily. It is totally separate from what the business does, or in the case of airlines where it flies. Its just a name and it is up to the owner to decide what the business is called and when (if ever) to change it. The names of airlines often come from the place that the airline started operations but there is no rule saying this must be so.
There is no rule stating you have to call the airline by the places it actually flies over. Generally changing names of businesses can confuse customers, so it is not done very often. I would think also that airlines are proud of their history so that's another reason not to rename just because they created a new route.