Popular, OSI-approved licenses include clauses like "Neither the name of the nor the names of its contributors may be used to endorse or promote products derived from this software" (BSD) or restrictions on the use of the original name (see Firefox/Iceweasel drama).
If you put in a clause like "You may not keep the software's name or support URL unless distributing an officially-released version", perhaps it would still be open-source as per OSI, and address those distribution issues? It's easy enough for distributors to patch in their own support mailing-list...