Hi,
Well, I think I might get what you're saying. Are you using the Text Pane to eliminate the position? If not, you could try this:

1. In the organization chart click on the box representing the position you want to eliminate.
2. Click on the Text Pane button. It's located in the "Create Graphic" group on the SmartArt Tools "Design" tab.
3. Place your cursor to the right of the person's name in the pane that pops up.
4. Backspace to delete the name.
5. Click to place the cursor somewhere else in the box, say by another name.
6. Click on the "Text Pane" button once again to close the pane.

Hope that helps!
Kara