Briefly, in the absence of some highly specific ontological commitment- i.e. a 'model'- neither what you believe to be your concept of a dog in your mind, nor the word 'dog' exist, or are capable of construction, as distinct, well defined, 'atomic propositions'- so to speak. On the contrary, both are highly subjective, ghostly, presences caught up in a web- a field- of complex interdependence and infinitely shifting boundaries.
Derrida's hauntology while affirming the death of the sort of metaphysics which holds that to have a well defined concept of one thing would involve having absolute knowledge of all things- since all things can be linked by a predicate relationship to any given thing- nevertheless insists that, for political or ethical reasons, it remains important to hold that the project really is worthwhile of thinking that thought is radically ontological and, thus, that the deconstruction of texts- to show that everything referred to is a shifting slippery sort of spectre, continually turning into its opposite- remains central to our concerns as intellectuals.
The acknowledgement of the infinite play of defer/differ ance leaves- at least on this naively optimistic reading- the signified a little freer than before, with more elbow room to make strategic alliances, and hence the method of deconstruction- though continuing the project of the death of metaphysics- nevertheless remains of interest or has some positive instrumentality.
Put simply, Derrida thought his distinctions worthwhile because they simultaneously undermined- or revealed symmetries between- both the Hegelian sort of philosophy as well as the analytical sort espoused by Quine and Kripke and so on. In other words it was 'a plague on both your houses'- so to speak- quite relevant at a time of the 'looking glass war' of ideologies back in the 60's and 70's and so on.
Focusing narrowly on your question- for it to make sense you have to subscribe to something like the Barcan-Kripke notion of Identity and the possibility of Kripkean rigid designators. But since names actually tend to function in a taxonomic sort of way- i.e. relating to a family or a class- the possibility of an actual concept or actual language behaving in the way you want- viz. 'dog' rigidly designating 'that dog I saw yesterday' and so on- might turn out to be zero. Alternatively, you might be able to work up an artificial language in which such statements are meaningful. However, those artificial languages might be very restricted in terms of what you could actually do with logical operators and hence not a viable counter-example.
At a common sense level- for I realize that what I wrote above aint exactly clear- you are saying why should there not be a fixed correlation between my saying 'dog' and the picture in my mind of the dog I saw yesterday? Answer- suppose the T.V comes on with a news report about rabid dogs- it may be that the mental picture you have of the dog you saw yesterday has changed a little. A contrary process could also be at play. As you say dog- a generic picture of 'dog' in the language flashes into your mind. That animal you saw briefly by twilight suddenly sharpens up in your mind's eye- pixels are added, a sort of rendering takes place which may itself have emotional overtones. In some societies, to see a black dog is an omen of imminent death. James Joyce- whom Derrida, like Lacan, studied carefully- has vividly demonstrated the very slippery nature of the semantic field under the seismic pressure of the emotional overtones of words.
However, this is a gross simplification of Derrida and perhaps hasn't answered your question at all. I'd better stop.