It's basically a different form of the cockpit glass errors people typically get. The problem is that the polygons making up the nameplate have to be rendered last. The only way to change it is to disconnect the nameplate polygons from the ship in truespace and then add them back into the ships object hierarchy as the last thing you do before conversion.
In short, just before conversion, do this:

If you really can't be bothered reconverting the whole thing, then just take the nameplate texture and turn it into a kind of billboard thing - ie, instead of having a transparent background to the nameplate apply a texture to it with the name on that texture.