Between Locke and Mill, I think I support Locke's views more, simply because I do not agree that names must refer to the physical things. In other words, I believe that some names do in fact refer to some abstract notion that does not have a grounding on concrete, physical things like Mill argues. Additionally, I think Locke's description of language requiring general terms, and that language cannot support a 1:1 ratio of specific words each referring to specific things, and that this fact about language extends beyond Proper names like Mill would argue.
Mill tries to circumvent this problem by saying that a certain phrases like "the king the succeeded William the Conqueror" refers to a specific person, and that even "the king" could refer to a certain person if said in the right context, but I don't find this argument more motivating than Locke's general terms. Mill's argument adds an unnecessary complication to language that Locke avoids.
With that said, Locke's argument is not perfect. Locke relies on the subjective interpretation each person has about the idea a word refers to and this could lead to complications and misunderstandings. When discussing complex ideas, relying on subjective understandings or interpretations is not strong enough to support nuanced discussions and requires some sort of objective restriction.
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