If it's the KML type, then that's the FME format attribute kml_name. You have it exposed in the reader, but then you need to connect it to something in the writer for it to get written.
Best solution is to use Manual for the output schema and add a new attribute (such as kmltype).
Then use an AttributeManager to rename the incoming kml_name to kmltype on the output.
Otherwise, can you see this attribute if you open up the KMZ in the FME Data Inspector? If you can't see it there then it's not going to come through the reader in Workbench. At that point perhaps open up the KML file in a text editor (the KMZ should simply be a zip file that you could extract the KML file from) and see if you can actually see it inside the file.
Other things you could do are to try the Scan Schema parameter on the reader (when you add the reader it should be set to Yes), and if that fails turn on the Verbose Logging parameter on the reader (which may give more info about what is going on).