While there is no way to remove the POI's that you mention from displaying (that I am aware of), there are a couple of alternatives that may be helpful.
Tap the Menu button, then "Settings" > "Navigation" > "Map View". Select "Split 2D Map" or "Split Birdview Map". Now you will have a split screen. You can zoom each side independently, which will allow for an overview on one side with a close-up view on the other. In effect, this removes the POI name from the close up view. One thing that I have noticed though is that the next street is not always named if it is a smaller street, even on a tight zoom. Here is a potential workaround.
Having selected your split view of choice, do the following:
Tap the Menu button > "Info" > "Where am I?". On the left hand side of the split screen appears the following (retaining your previous map view selection on the right side):
Next street
Distance to the next intersection
Current street
Previous street
Distance traveled from the previous intersection
This can come in handy for a couple of reasons. As you drive, you will always know the name of street at your next intersection (exception - different street names to right and left). Also, if you are in need of roadside assistance, this information will be useful to that provider.
Not exactly what you wanted, but I hope that it helps.