Not only dissolving the shape but merging the attributes

[GordonBaker]

I dissolve overlapping polygons to determine where they overlap. The shapes that dissolve are correct. The next step I want is to merge the records into 1 polygon. My problem is when 2 polygons overlap it creates 2 identical shapes polygons. The only difference is the attribute data behind it. Can I somehow combine the attribute data into a single polygon, that says Circle1,Circle2?  The picture I uploaded may aid in my query.

[DanPatterson_Retired]

Dissolve—Data Management toolbox | ArcGIS Desktop 

For text, you are only given the option to use first or last.  You could always try a spatial or attribute join back of missing attributes if needed.

[DuncanHornby]

If you used Delete Identical tool using the SHAPE field that would remove duplicated geometries, so removing "stacked geometries".

As Dan Patterson suggests you can join data back to the polygons. A trick I use is to extract the centroid, then concatenate the XY coordinate into a single string field this then becomes a unique ID for the point that always sits inside your polygon. You can then hook into this ID for joining data back to it.