There are many kinds of psychological disorders where the patient is "directly confronted" with the diagnosis or even knows it before he or she contacts the therapist. These disorders include, but are not limited to, pedophilia, eating disorders, post traumatic stress disorder, substance dependence and phobias.
For example, a person seeking help because he is afraid of flying knows perfectly well what he is being treated for. Similarly, heroin addicts are not left in doubt about the focus of their treatment. In fact, psychoeducation, i.e. the explanation of the causes, symptoms, prevalence and treatment of a disorder, is a common part of cognitive behavioral therapy of almost all disorders and a basic element in its effectiveness.
The problem, as Nick already mentioned, is that often, especially with personality disorders, it is not completely clear what the patient is actually suffering from, and that giving a definite diagnosis is simply impossible. Depending on the type of therapy, a therapist will likely explain this difficulty and not be secretive about it. In our psychological day care clinic all patients know their diagnosis, from depression to enuresis to internet addiction – though of course not all patients accept the diagnosis they are given, and (see what Nick wrote about reactance) many abort their treatment because of a lack of self-insight!
Psychoanalysis is a bit different in that the therapist attempts to be a neutral plane for the projections of the patient, and therefore often avoids delimiting statements. Here, not giving a diagnosis may be part of the therapy, although of course the patient has the (legal) right to receive it, if he so insists. A psychoanalyst might answer to the patient's complaint that he did not get a diagnosis with: "You only have to ask me for it." And then, quite usually, the patient avoids this direct inquiry, and the therapy turns to the reason why the patient complains and avoids to demand what is his right to know.