No, I did not launch the kernels in front of the calculation, but it is a goog idea especially when there are more tasks that should run in parallel.
Nevertheless, I am still seeking for a (fast) ParallelTable solution. With the following lines of code I extract the MonthName and DayName from the dataset. Without other changes only these two lines of code deliver currently the needed results.
mvtMonth = Table[DateString[data[[n, 2]], {"MonthName"}], {n, 1, nrows}];
mvtWeekday = Table[DateString[data[[n, 2]], {"DayName"}], {n, 1, nrows}];
Map has difficulties with the Dataset and ParallelTable runs "forever". So, I can continue with my work, but I am still not happy with the calculation speed.