"Among the" is a typo or misprint. It should say "among them". The correct version can be seen here:
The objective of the assessment process is to conduct a comprehensive analysis of the patient's personality dynamics and the relationship among them, what Adler called the style of life. (source)
(The choice between a dash and a comma is unimportant here. There is nothing wrong with using a dash here.)
I take this to mean that Adler used the term "style of life" to refer to the patient's personality dynamics and the relationship among them.
However, it is conceivable that the term "style of life" only refers to the relationship among them, not the dynamics themselves. You'd have to read and understand more about Adler's work to be certain. I don't think it refers back to the comprehensive analysis, since that has an indefinite article preceding it, which wouldn't fit well with the definite article before "style of life".