Ambiguous proper names

Earlier, I suggested that the problem of when a person is thinking about X – which involves the difficult question of empirically unobservable entities such as ‘thoughts’, can be reduced to the apparently simpler problem of when two occurrences of a proper name have the same sense or meaning. Specifically

(*) Tom has a thought about Sherlock Holmes

is true if and only if Tom has a thought which, if expressed, would contain a term synonymous with the name ‘Sherlock Holmes’ as it occurs in the sentence above (*). The problem is now to explain when any occurrence of the name ‘Sherlock Holmes’, has the same meaning as used above. This would be simple question to resolve if proper names always had the same meaning. Clearly in the ‘Sherlock Holmes’ stories it does. Conan Doyle uses it only to refer to the same fictional detective. But as I noted here, there is a living person called 'Sherlock Holmes' (a minister of the church in Massachusetts, America). If Tom is having a thought about the fictional detective, and if by 'Sherlock Holmes' above (*) I mean that person living in Massachusetts, then (*) is false. So how do we determine when proper names are not being used ambiguously? What do we mean by ‘having the same sense’? Isn’t this almost as difficult as explaining when two thoughts are the same?