You have to duplicate the templates in the project panel not in the timeline. That is the only way to make a unique copy of a nested comp.
I tried that, but it didn't work. Specifically, 1) I chose/highlighted the project panel. 2) I highlighted the clip I wanted to duplicate. 3) I clicked on edit. 4) I clicked on duplicate. 5) A copy of that clip did indeed come up in the panel & rather than a"1" at the end, it had a "2" so I assume that is considered "renamed.". 6) I dragged the original clip to the timeline. 7) I dragged the copy to the timeline. 8) I inserted one of my photos in the 1st "frame." 9) I checked the "frame" in the 2nd clip and it TOO had that same photo even though I had not yet inserted a photo.
Are you duplicating footage or pre-comps. Highlighted the clip is meaningless. Assets in the composition panel are either footage or compositions. Footage can be stills, audio, or video. Sorry, but you're attempting to do something without any knowledge of how footage or comps work. If it's footage, then your workflow is flawed. You need to duplicate the layer in the Timeline and then replace the footage in the duplicate by holding down the Alt/Option key and dragging the new footage to the selected footage in the timeline. If it is a pre-comp then you have to add your new footage to the pre-comp, not the footage layer.
Here's what you should do, Show us the main composition timeline and a mini flow chart with the properties of your problem layers revealed. Just select them in the timeline and press the U key twice. Since there are millions of ways to create a slideshow we can't possibly know what to tell you to do without seeing the composition and the timeline and the flow chart. There are hundreds of slide show templates on the web, most from well meaning but inexperienced folks trying to improve their standing in the AE community. Most don't have sufficient documentation, and most that I've looked at are a real mess to customize. Without knowing exactly where you are starting from we have no idea what to suggest except that your workflow is wrong and you need to make sure that every layer in the project is unique.
If it were me and I had access to Lightroom or iPhoto I would throw the stills in one of those apps and generate a slide show, That will take about 10 minutes. Render that and then when that's done, either import it into Premiere Pro to add titles. Then, when that's done and I've covered myself for offering to produce the video, I would move into After Effects and try and figure out how to do more of a custom job. One more hint, if the Photos are all much larger than your HD comp then you should batch resize them. All still images in an After Effects composition should be at or near 100% scale at some point in the project, or if 3D layers not closer to the camera than the Zoom value of the camera. At no time should still images be sitting still in a composition with a scale value of more than about 130% or closer to the camera than 60% of the zoom value.
Thanks for the help! I'll try that to get myself covered. I am far more experienced with Pr than AE, so that's a good idea.