Here I want to suggest one reason why people have had trouble seeing a middle way between descriptivism and Millianism about names - that is, why my sort of view of names has not already prevailed or at least become a prominent option. (It is far from the only reason, and I will consider others in future posts.) This may also afford us some insight into why both descriptivists and Millians endorse their respective views.
The articulation assumption is that, if you say that names have meanings beyond their referents, you have to be able, at least in principle, to specify what they are, and in some way which articulates or unpacks these meanings. The assumption is at work in B's role in this short dialogue:
A: Names have meanings over and above their bearers.
B: What's the meaning of 'John Nash', then?
I am envisaging B's reply here as a Millian-leaning attempt to embarrass A out of their assertion.
And what I want to say here is that A need not have anything to reply here, in order to have respectably made their assertion.
To see this, it helps to reflect that, in saying 'what the meaning of' an expression is, what we are doing is giving, or at least referring to, an expression which has the same meaning as the one whose meaning is in question. And there is no reason why a name like 'John Nash' needs to be synonymous with any other expression, let alone one with more structure (so that it could be said to articulate or unpack the meaning of 'John Nash').
One of the functions of semantic notions is to bundle and separate
instances of expressions. We bundle by ascribing the same meaning, we
separate by ascribing different meanings.
Frege, who notoriously says precious little about his senses, at one point says that the sense of 'Aristotle' might be: the teacher of Alexander. (I reproduce his style of formulation, using a colon and no quote marks, but I don't mean to say this is clear and unambiguous.) But we don't need to do any such thing.
Making the articulation assumption could be one of the forces pushing thinkers who are impressed by anti-descriptivist arguments, such as Kripke's, toward Millianism. Likewise, it could be one of the forces pushing thinkers who are impressed by anti-Millian considerations, such as the apparent difference in meaning between 'Hesperus is Hesperus' and 'Hesperus is Phosphorus' and the apparent meaningfulness true singular negative existentials like 'Santa doesn't exist', toward (perhaps sophisticated) forms of descriptivism.
Once you reflect that the articulation assumption is false, it becomes clear that there is a middle way, quite immune to both sets of problems.