Saving multiple versions of a file with different names in one action to the same folder

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Also - why cant a step backwards (while recording an action) after a "save as" then step backwards?  Neither the keyboard nor the commands are recording, even though the red light is on and the changes are happening on the screen, the undo to a previous state does not register in the recorded action.

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By @RAB123

For "Undo" use "Insert Menu Item..." in Actions panel.

You can use the Image Processor Pro Plug-in Script to do what you want to do.  Record it in an action in an old version of Photoshop.  The current versions of Photoshop no longer record Images Processor Pro actions step correctly.  Old versions of Photoshop do. You are not required to use Image Processor Pro in an action you cans use it from Bridge menu Tools>Photoshop>Image Processor Pro... or from  Photoshop menu File>Automate>Image Prtocessor Pro... and use Images Processor Pro... Dialog.  You can save the Dialog's settings to use and load them the next time you use the plug-in so you do not have to set up all 10 output files each tine you use Image Processor Pro Dialog. All image will retain their Aspect Ratio and be resized to fit within the canvas size set for the output file types.

Do you have non-linear history on?

I always use an explicit snapshot that you need to revert to.

As for varying filenames, you would need a script for that.

Without creating a custom script, you may be able to achieve what you need using the fantastic Image Processor Pro script:

Image Processor Pro / v3_2 betas