It's a bit more complicated than you've been led to believe.

The _number_ in Caller ID is sent along with the "setup" of the phone
call, so is available to the final central office (and to the receiving
phone if CNID is unblocked) at the exact same time.

However, the _name_ is NOT sent the same way. Rather, the receiving
central office (or, more likely, some intermediate gateway, but let's not
go there) gets the number and does a _reverse_ database lookup.

Now the actual databse in use is, well, somewhere or another. If you're
calling from inside a traditional wireline telco RBOC to another phone in
the same company, they've got the billing/directory info in house and you
get it accurately.

On the other hand, if there's a long distance call involved to a different
company, well all bets are off. The company receiving the call has to know
where to do the database dip, _and_ that often is NOT the place the call
came from.

Why? two reasons:

    a) the originating company charges for the database dip. The
    receiving company doesn't want to pay, so they'll look for
    a secondary, and cheaper (and often less accurate) provider.

        NOTE that this is similar to the problem nowadays
        when you make a "directory assistance" call...

    b) maintaining that data base, and making it available
    for instant lookup, isn't that eay. So some places
    will hand it off to a third party.

Oh, and for good measure, if there'e number portability involved
and the riginating phone has moved from the company that used to
"own" the prefix to another, there are plenty of headachess...