What is the correct term for this external telephone wire cover? I have searched for external telephone cover and similar terms but can't see one to order.
It was once a brand name (and still is) but you'll often hear covers of this sort called Wiremold, which also describes the rectangular wiring cover below the box. In my years of cable television, I've probably seen dozens of different designs of telephone covers. I would expect that you may not find an exact match, unless you happen across new-old-stock somewhere.
My quick Google search shows that even Google considers Wiremold to be a generic term for plastic wire routing covers, typically surface mounted.
Most of the US telephone companies combine the cover with the demark with terminology to indicate that it's the "consumer interface module" or similar wording.
Because it's low voltage wiring, it's also unlikely that your zoning codes have specific requirements. You should be able to find something to your liking in a big box store or online, searching wiremold telephone cover.