Paul, You have asked two good questions.
As I look back over my notes I do not see any plausible way that I could have detected these issues earlier in therapy. Gary had given only very subtle indications of his suspicious outlook until this point in therapy. Even though I was writing a book chapter on CT with paranoid personality disorder at the time, I did not spot it.
Why? My theory is that Gary knew from previous experience that others saw his suspicions as paranoid and that he made a point of not revealing them until he decided that I was OK.
One of the strengths of a formulation-based approach is that if I base my interventions on my understanding of the client and they work the way I would expect, that suggests that my understanding of the client is adequate. If the interventions do not work the way I expect, then by taking a look at the client's thoughts, feelings, and actions at that point we can figure out if our initial formulation is inadequate and, if so, revise it. Ideally, this makes therapy a self-correcting process.
How would Gary react to the lable? Since he is not familiar with DSM, he would not know what the label means but would not like the sound of it. If I read the diagnostic criteria to him, I think he would say that it is a pretty good fit.
No, I do not think that it would be very helpful (or harmful) to share this diagnostic label with Gary. If he asked, I would discuss it with him but I doubt if I would bring it up. It might be helpful to Gary if he were to have a concise summary of this part of his problems but a brief behavioral description (such as "I tend to be guarded and suspicious and that often causes problems for me") would be more useful that a diagnostic label.
The diagnostic label can be useful to Gary's therapist if the label helps the therapist to access useful information about treating people like Gary (such as book chapters about Cognitive Therapy with paranoid personality disorder). Once I recognized Gary's paranioa, I did not have to start from scratch in developing a formulation, I could start with general ideas regarding paranoid personality disorder and then tailor them to Gary.