Jepps airport and VOR names ... how used?

I agree it is ambigous. ATC can use either VOR name or 3 letter ID.

Airport names are a mess also. Take "Jeffco" (KBJC). It is listed as
being in Denver in the Approach plates (at least the govt ones). But it
is not in Denver (it is in the Denver area but is actually in
Westminster (I think)). There are many airports like this. Especially
confusing when you aren't prepared for it in advance (like a
diversion).

You think thats a mess, in Alaska, many of the airports have TWO
different id codes or did, they are working to clear that up)...

Such is life.