Steven Pinker says in The Stuff of Thought (p. 8-9), “Certainly a word meaning depends on something inside the head… however a word is learned, it must leave some trace in the brain. The meaning of a word, then, seems to consist of information stored in the heads of the people who know the word: the elementary concepts that define it, and for a concrete word, an image of what it refers to.”
But Pinker goes on to say names are different: (p. 10) “A name points to a person in the world in the same way that I can point to a rock in front of me right now. The name is meaningful to us because of an unbroken chain of word of mouth (or word of pen) that links the word we now use to the original act of christening. We will see that it’s not just names, but words for many kinds of things, that are rigidly yoked to the world by acts of pointing, dubbing, and sticking rather than being stipulated in a definition.”
Now these two relations between names and things differ. For any given person at a given time, they may have an meaning in their head for a word. Then I say there is a relation R|S between the person and an object.
If the word is ‘Tom’ and the object is Tom, this means there is an idea_of_tom in the persons brain, and
‘Tom’ R idea_of_tom
and
idea_of_tom S Tom
Here R is a relation between names and ideas and S is a relation between ideas and things.
In cases where another person also has a relation R|S between ‘Tom’ and Tom, they would not have identical ideas (they have different brains). The causal chain for both, it would seem, would, although different, go back to the same act of christening.
However, there could be other people named ‘Tom’ or other names, from other acts of christening, for Tom.
Suppose ‘Jack’ is another name for Tom.
Then Jack = Tom (for anyone knowing both christenings were of the same person).
But it could be believed that Jack ~= Tom by anyone not knowing the two christenings were of the same person. The causal links from the two christenings to the two idea (traces in the brain) are different.
Also note that although it would have to be a very rare coincidence for there to be separate acts of christening of the same thing with the same name, the causal chains will be very different most of the time. There need be no trace of the original christening in the brain of the person who knows the name of an object.
This explained more fully at Dennis J. Darland’s Philosophy