Unfortunately, Picasa doesn't have such an option. But, you can write the tags of the people in the metadata of the picture. This way, you can use another tool to obtain those names. To do this, open Picasa and go under Tools > Options > Name Tags and make sure that Store name tags in photos option is selected. After you did this, go under Tools > Experimental > Write Faces to XMP. This option will write the tags in the picture's metadata. To view the picture's data, you can use a tool from the Software Informer's database. I suggest you take a look at ExifToolGUI.
