OK, this is quite simple - less than five minutes, which I know because I created a movie demonstrating it:
To give the steps in more detail here...
1) The source filename information comes from the source dataset parameter (say SourceDataset_ACAD) in the Navigator window
2) Put down a FileNamePartExtractor transformer to break down that source dataset parameter into its component parts, eg dirpath and filename
3) For MyFolder (which I assume the user gets to enter) create a new published/user parameter that lets the user enter a filename.
4) Go to the Navigator window and look for Dataset Fanout for the ACAD output. Turn it on and set the fanout expression to be:
5. Run the translation. Enter a MyFolder value. If the data was originally C:\FMEData2016\Data\Transportation\Roads.dwg, and MyFolder is called "Mark", then the output will be C:\FMEData2016\Data\Transportation\Mark\Roads.dwg
Another thing you could do (for example) is use the TimeStamper transformer to create a timestamp and incorporate that into the file/path name of the output. That way each output is timestamped in its name. Lots of possibilities.