The article contains several applications of the version of the historical theory of proper names presented in the previous article (see [11]). They are designed to defend its epistemologically meager point of view (referring to things via names does not presuppose any other epistemological contact with the things). It is argued that the distinction between reference of an expression and that of a speaker which lies in the very heart of the theory enables one to handle with many well-known examples (e.g. Kripke’s “Gödel”/“Schmidt” and “Feynman”/“Gell-Mann” cases). Then bounds of referential uses of proper names are tested with respect to some other examples as well (e.g. Evans’ “Madagascar” and Yagisawa’s “Spot”/“Garf” cases). The point is that the theory is neither too narrow nor too broad: it does not exclude, on the one hand, those uses of a name that are demonstrably referrential and it does not, on the other hand, count as referring clearly non-referrential “uses” of a name.