If there is an on-ramp to the road, that ramp can and should be named to match any signs. So you can have the road itself named "So-and-So Expy N" but the ramps can be labeled to say "to US-999 N". Or the other way around depending on the situation: road = "US-999 N" and signs = "to So-and-So Expy N".
If there are not ramps to the road in question (highway running along surface streets through a town), then we are still stuck. In that case, the name that is most used by people/shown on all the signs should be used.
So for either case, your situation
may be able to be solved through some editing of the maps (which you yourself can do, check the
wiki).
We did give this topic some time at the meetup in Palo Alto this past weekend, so Waze knows we want more control. We will have to see if they come up with anything to help us.