As suggested i post my commend as an answer:
I made a bugreport on this (March 27) and got an answer from WRI 3 days later that says:
In this case, Mathematica is behaving as designed. In particular, the StyleNames item does not apply to the cells you are looking at. Further, StyleNames is an undocumented symbol, meaning that it's usage can change without warning. In this particular case, however, if you simply ask for the current value of StyleNames for a given cell, you get back an empty list. Please see the attached notebook for details.
The content of the attached notebook is as followes:
StyleNames is undocumented
Here is the command you used to create a notebook, simplified a little bit.
nb = CreateDocument[{TextCell["abc", "Section"]}]
The following extracts a cell object.
cell = Cells[nb, CellStyle -> "Section"][[1]]
CurrentValue of cell returns nothing for StyleNames
CurrentValue[cell, StyleNames]
StyleNames is undocumented functionality.
?StyleNames
Out:
System`StyleNames
Attributes[StyleNames] = {Protected}
For me this answer was not very satisfying. In summary they just told me that StyleNames is undocumented and that it cannot be used to change Styles.
From my interpretation it's a value for extra Styles.
CurrentValue[cell, StyleNames] = "MyStyle"
is not meant to change the current Style rather than add "MyStyle" to the existing styles of a cell. (my interpretation)
What i've learned from this, is that you cannot trust in the functionality of an undocumented Symbol like StyleNames, because it's functionality is not clear and can change without warning!
I can also recommend to contact WRI for possible bugs, they where very fast and polite and gave me many thanks for my email.
Use: support AT wolfram DOT com for sending bugreport to WRI.
EDIT:
I a further Email i wrote WRI that the example in the documentation of Cells(Applications) is very missleading, because it makes you think, that StyleNames is for changing the cell Style. The friendly WRI-guy told me that he made a report on this part of the documentation.
WORK AROUNDS
See this answer: by kuba for 3 different ways to change to CellStyle!