Which process step in KDD or CRISP-DM includes labeling of the data? KDD and CRISP-DM are both processes to structure your Data Mining procedure. Is data labeling not also a important part of Data Mining? 

Data labeling is for example in unsupervised learning the target of the Data Mining process. So if I want to classify a data set that was labelled by me before, do I just do the process twice? In my opinion sometimes the labeling is quite trivial, so that doing the process twice would be quite unnecessary? 

Is it possible to include the labeling into the data exploring or preprocessing phase? E.g. in CRISP-DM Preprocessing there is something like generating a new parameter. Can this Parameter be also a new target/label? 

I know this question is quite process orientated and in Data Mining you are quite free but just assume that in this case you have to follow the process.
Data Labeling is a very trivial process as you have mentioned.

As far as I know, it falls under Data Understanding(Exploration Analysis). When you don't know anything about data then you do exploratory analysis to understand and derive some insights. If you don't know the target variable then the problem falls under Unsupervised Learning, as you have mentioned in the question that your problem is unsupervised. So, you don't know your Target Variable, you are trying to make new feature/dimension to get some good insight irrespective of the factor whether you derive your Target Variable or any other feature it falls under Data Preparation(any new derived variables), which ever we think are important for our Analysis