The trans-Neptunian planetoid 2002 MS4 is currently the largest known unnamed Sun-orbiting object. Is there any standard schedule on when this and similar objects might be named? Usually the discoverers propose the names for the celestial body, which Chad Trujillo and Michael Brown obiously haven't. In that case, what will happen?
If the discoverers don't propose a name (and they have a 10 year interval in which to do so) then the object remains unnamed.
This minor solar system body has a permanent designation, "307261" which uniquely identifies it. So there is no need for a name. There is no provision for the IAU to grant the naming rights to a third person, and certainly the naming rights aren't auctioned or available for sale.
So if the discoverers don't name it, it remains known only by its numeric code.
See https://www.iau.org/public/themes/naming/ section "Minor Planets"