Frege's semantic account of names – that is, proper names and definite descriptions – is a distinguished piece of philosophical analysis and can be considered a classic in its field. There is, however, a considerable amount of disagreement about which basic issues it treats. Although it is generally accepted that the reference of a name is the object designated by it, critics often claim that Frege's general notion of reference is tied too closely to the name-bearer relation. For instance, Kneale complains that Frege “tries to explain the use of all words and other signs by consideration of what is involved in naming” and claims that Frege was led to his theory of sense and reference “by his preoccupation with names and quasi-names”. Even Dummett is convinced that the name-bearer relation has to be considered a “prototype” for Frege's theory of reference. According to my view, all the interpretations of this theory that claim a prominent role for that relation are wrong, as I have shown for his theory of the reference of sentences and as I shall show now for his account of the reference of names.

Most of Frege's critics reject his theory of the sense of names. There is strong disagreement about what the sense of a name is supposed to be, and there are many who reject his claim that every name has a sense.