Thank you for your reply, Lance! I looked at the link you sent and all the polygons in the example seem to be spatially adjacent to one another. Our polygons are scattered about spatially, but they do share a common name for the areas they "cover."
The tool will still work for non-adjacent features just make sure you select the "Create multipart features" check box. You would set "cover", or whatever the name of the common attribute, as your Dissolve Field.