If two names, "N1" and "N2", are introduced into the language for exactly the same purpose, but are made known to a speaker, S, in different circumstances, then it's possible for the sentences "S believes that N1 = N1" and "S believes that N1 = N2" to have different truth-values. How is this possible on an externalist theory of concepts?
Here's an example:
Suppose that the ancients introduced the names "Hesperus" and "The Evening Star" into the language by pointing to the relevant object in the evening sky and declaring "We hereby name that object 'Hesperus' and 'The Evening Star'".
Now scroll forward however many centuries, and suppose that the name "The Evening Star" is made known to Dave by his mother, when she points to the relevant object in the evening sky and tells him "That's called 'The Evening Star'".
Suppose further that the name "Hesperus" is made known to Dave by his schoolteacher, when he tells Dave "Another name for the planet Venus is 'Hesperus'".
Dave makes no association between what his mother has told him and what his schoolteacher has told him, and so he doesn't believe that The Evening Star is Hesperus, even though he believes wholeheartedly that The Evening Star is The Evening Star and Hesperus is Hesperus.