I am going to assume that you have the org charts created and populated using the Shape Data so that names, positions etc are entered into the relevant metadata fields.

So then you can do this by either:
1. Editing the master shape on the document stencil to remove the Name field from the text box or
2. Having a different shape available in a stencil which includes only the text fields you want to retain. You can then select all the boxes and 'Change Shape' to swap in the preferred text content.

__________________
Andrew Lockton
Chrysalis Design, Melbourne Australia