What Makes Someone Become the Unique Person Who They Are ?
With the example of being the only person with blonde hair, it would affect a person but only as one aspect of many others. Such aspects as being even in a group and being the tallest, smallest or oldest are all significant. As it is, most people in many groups simultaneously, the first one being the family, which is likely to have a large consequence in shaping who one becomes. There are also those who are famous, such as singers, writers and footballers. Their experience could even lead to an inflated ego, or sense of being special.
It is all constructed subjectively, as you say. It is possible for there to be large discrepancies in how a person sees themselves to how they are seen by others. For instance, it is possible to feel ugly while being seen as attractive by others.
And, it is about the inner aspects of the self, going back to the 'I' of Descartes. That is about how one witnesses consciousness and is able to stand back and reflect. It is hard to imagine what it means to be another person, although, of course, people exchange their experiences and find common ground.
The culture of individualism was also important in the development of the sense of self. This may include all kinds of parts of life, including pursuing social markers of success and those through acquisitions. Social roles, like being married or divorced maybe crucial too. There are also the mythic aspects too, in the process of individuation. However, there may be opposite processes in the twentieth first century whereby individuals' identity are being diminished, with people being treated more as numbers.