This seems like a limitation of barcodesinc.com. They're the ones outputting the image. If they allow another parameter for "additional title", you could stick the value in there. But Google Sheets don't have features to modify a picture that is output by another site.
Google Sheets don't seem to allow you to concatenate text with an image in the same cell; ...
I think it's possible, if you look at the Trello API for writing cards. For starters, you'd have to make your board public, and your QR code would obviously have to make a POST request.
Kudos on an interesting idea, though; I would love to know how it turns out! Also, I would've normally posted this as a comment but I didn't have enough rep to do that.