In your opinion (supported by references or not), what differences are needed to qualify a theory as different enough from an existing theory to justify giving it a new name?
Good question! Certainly relevant changes in underlying axioms should qualify, at least if those changes cause different derivations. Obviously relevant changes in the laws of existing theory qualify.
This is surely not a matter of terminology or mixing new terminological terms together, which resembles 'fashions of scientific research'. For deserving the criterion: new theory=new name, a fundamental innovation of the thought structure of a discipline is required, so we are dealing with rare events in the history of scientific research. I would welcome such a 'quantum leap' in medicine, economics and pedagogy, to balance wealth and health.