adobe photoshop - controlling save name when using action to batch process and save

I am trying to control filename when saving via an action.

Let's start with an image open on screen. It is called "image1.png". I press record to start the action. I run a greyscale filter. I then use save as and save it (in the same directory I got the original image from" as "image1_greyscale.png". Then I close image on screen and stop recording image.

Problem is when I use it on any other image eg "imagetwo.png", it also saves as "image1_greyscale.png". Which is wrong. I would prefer if I could get the action to save as something like;

"originalfilename" + "_greyscale".png

I want to batch process large amounts of files and have their greyscale versions output correctly. All help appreciated!

(I could get something like what i need through the batch tab, but that would mean every time I change between batches i need to correctly set the filename change, I would much rather have it hardcoded directly into the action itself)