If you are writing to a a file-based format such as GML, DWG, DGN, etc. (formats that have a way to assign data to different layers within a single file), then use a TimeStamper in conjunction with a dataset fanout. The TimeStamper will add a date attribute to your features, and the dataset fanout will separate your files based on that date value (see Date_in_filename_example1.fmwt):
If you are writing to a folder-based format such as SHAPE, TAB, etc. (formats that DO NOT have a way to assign data to different layers within a single file), then use a TimeStamper in conjunction with a feature-type fanout. The TimeStamper will add a date attribute to our features, and the feature-type fanout will separate your files based on that date value (see Date_in_filename_example2.fmwt):
For more information on fanouts see:
http://fmepedia.safe.com/articles/How_To/Fanout