I believe I understand where you're coming from. Typically, a label is given in order to help pinpoint a specific course of action. So, if no label then we can be left wondering 'What's the specific course of action? What exactly is the specialist treating?' No label can leave us feeling a little up in the air without direction.
Not sure if this helps but the following may offer another way of looking at things. A few years back, a friend of mine was treated for a lump in her breast that was acknowledged as being pre-cancerous. Treatment: The lump was removed and she underwent some radiotherapy sessions. Problem solved based on this course of action. With yourself, perhaps it could make sense to say that you are in a possible pre-depression stage or pre-anxiety stage. If you are not treated now, who is not to say you won't eventually face full-blown depression and anxiety. You're at a vital point of investigation and treatment.
A specific label must apply to a specific condition or behaviour (of the brain and/or body) in order for the best course of action to be determined. Clinical depression, for example, is complex; it involves evidence of particular thought patterns, particular changes in chemistry etc. Depression can be a life altering condition that impacts just about every area in life. It can impact not only our level of happiness and self-esteem, it can also impact our level of energy and motivation, our ability to manage emotions, our ability to experience healthy relationships, our sense of connection to life itself as well as so many other things. I experienced depression for some years in the earlier part of my life and it is intensely different to the self-esteem and sometimes deeply challenging emotional issues that can present in my life these days. I personally found depression to be overwhelming and debilitating. I wish I'd received help in the stages leading up to my depression.
The brain is a complex thing. We don't necessarily need labels in order to navigate such complexity; sometimes support and guidance can be positively life-changing.
Take care Wonderlands
By the way, as far as therapists go, some are quite happy to hand out labels and
meds without too much initial investigation whereas others are very
careful in how they diagnose their clients (which can pay off in the
long run). As your therapist gets to know you a bit better, as you open
up a bit more, their diagnosis or course of action may change.