You edited your question to add:

I wouldn't mind binary distributions of derivatives, however under a different name.

That adds the possibility of a free software (that is open source) answer to the original 'shared source' or 'shareware' question.

There are free software licenses that seem to require the name to be changed.

I may be wrong. Ask your lawyer about the Mozilla Public License

 This License does not grant any rights in the trademarks, service marks,
 or logos of any Contributor (except as may be necessary to comply with
 the notice requirements in Section 3.4).

Sometimes, redistributors might not read your license, or make a very small change to your trademark. You might want to consider how difficult your restrictions may be to enforce, especially outside your home country.

You commented on your question to add:

I wouldn't mind binary distributions of derivatives, however under a different name.

That adds the possibility of a free software (that is open source) answer to the original 'shared source' or 'shareware' question.

There are free software licenses that seem to require the name to be changed.

I may be wrong. Ask your lawyer about the Mozilla Public License

 This License does not grant any rights in the trademarks, service marks,
 or logos of any Contributor (except as may be necessary to comply with
 the notice requirements in Section 3.4).

Sometimes, redistributors might not read your license, or make a very small change to your trademark. You might want to consider how difficult your restrictions may be to enforce, especially outside your home country.