Would it be possible to be evaluated for both in the same session? Or would they need to be separate?

I think it's important to recognize that diagnoses for psychological disorders/etc is not as exact or definite as we would probably like to believe. The disorders listed in the DSM for instance describe collections of surface phenomena that don't really scratch the surface of the underlying causes. A lot of it we still just don't understand, and our current understanding constantly changes, which is why you see these diagnostic criteria and diagnostic labels being updated and changed over time. It's very difficult to tease out sometimes what the best label might be for the specific symptoms an individual is experiencing, because you are absolutely right that there are a lot of similarities between psychological disorders. A lot of new diagnoses in the DSM-V were also found to lack scientific validity before it was even properly published, so I personally think that the value of finding the one "correct" diagnosis can sometimes be an endless and unsatisfying journey, as sometimes these diagnostic labels hold very little meaning in the end. It has been my experience that focusing on the symptoms and difficulties you are experiencing, and properly and specifically addressing those, rather than getting caught up in trying to find a diagnostic label, can be more helpful in the long run. Of course, I don't know all the specifics of your experience so your mileage may vary. I will say that I am pretty sure that the more extensive of testing you go through, the more professionals are able to do differential diagnoses by looking for those little differences between diagnostic labels, and make a more accurate guess as to what is going on.

I went to a neurologist. My testing was broken up into 2 days and the results took 2 weeks. It was on a military post so I got an appointment in a week. Warning, the first appointment can take up to 5 months to get in, some even longer and insurance policy can change. I got in quickly because only military families can see this doctor and not everyone in the area so mine had more openings and less patients.

I always read up on a diagnosis that my psychologist is considering and he asks what I feel about it before going ahead. Even asking me if I am okay with the diagnosis before making it official. I would highly recommend doing your own research, though. There are a lot of books that share multiple experiences from various people and that can provide a better perspective than the pros sometimes

And don't be afraid to self advocate. My doctor still scratches his head that with my list, I do not have BPD. Or DID. As stated above, their book is not even a true outline that applies to the majority of patients. Still, some of them use it as a bible and end up scratching their heads when it does not make sense.