I would be interested in that too. I frequently do a similar thing for a website, saving one inventory item photo 400×268 and a thumbnail 180×120 with a minor name change adding _s to the end of the thumbnail file. If I record an action and touch the file name at all, it saves that file name permanently with the action. No help.
My solution right now is to use Thumbs Plus. I run the a batch action on all my photos in Photoshop (or from Bridge) to shadow/highlight, levels, crop, and save for web to create the bigger photo, then run a Thumbs Plus resize batch on all of them. Thumbs Plus allows the file name to be altered in the batch.
A workaround that would work good only using Adobe products (but probably not for an existing website)would be to save each file size in a different subdirectory with the same name. I.E.:
Photos_300
Photos_200
Photos_100
Photos_50
The action can be set up to do multiple saves to different directories no problem.
Kirk
In short, "No, you can’t do what you want [file name-wise] if you try to modify the file name when the action is recorded." This applies to using Save for Web or Save as… [.jpg]. Just the way it works.
If resulting file sizes from Save as… [.jpg] are satisfactory, then file name modifications can be applied automatically if the action is invoked by the Batch command. In this case you would need an action for each output file size. Each action would be invoked by a batch command where the file name settings could be made. (If you use Save for Web in an action invoked by the Batch command, File Naming settings are ignored. SFW is a strange creature).
With today’s faster download speeds some feel the flexibility of using Save as… [.jpg] outweigh somewhat smaller file sizes created by SFW.
If you must use SFW, again you will need separate actions. Note the destination folder recorded in the action is fixed; it cannot be overridden in the batch command as is the case if Save as… [.jpg] is used. Once you apply each action using the batch command, the resulting files can be renamed using Bridge or an outside utility.
Kirk’s suggestion (3rd party tool) is a good one, too.
Long, ugly answer to what should be an easy process in PS.