Can I batch process different text to each photo?

You can do that using Data Sets as already mentioned (Variables).

You will nedd txt file with data (badge names) and layer in Photoshop which is associated with that data through variable name (top row in data set file and Image > Variables > Define in Ps with text layer selected).

Here is official help page https://helpx.adobe.com/photoshop/using/creating-data-driven-graphics.html

You somehow need to get the text for each badge and the image for each badges associated with each other. Then you can automate the process of creating the badges by creating  a badge template that will be used and be populated by some automate process.  That Process could be a Photoshop Feature like Photoshop Data Driven Graphics where Template layers  defined as variables are populated using a CSV file that associate Image layer and texts layer content.  It could be  a custom script you create that populate the badge template with your Images and add a text layer using the Image File's meta data you added added to each file; Or you could use  one of my Batch Collage scripts where you populate a Collage template with your Images and add a text layer using data you added to each Image File Name.

Image > Variables in Photoshop.

Photoshop, Illustrator and InDesign (data merge) all have them... Which program is the best choice will depend.