can I add a hidden Shopify "tag" to a form so that all form submission will have the same tag?

Hello,

I couldn't understand your question clearly. As I understand you want a field that will allow you to mark your submissions. You can add a hidden text field to mark all of your submissions as you want.

After adding the field you can insert your tag and hide that field. The filed won't be seen on the form. Please see the screen-cast:

If this is not your question please elaborate your issue further. 

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Regards.

On behalf of my colleague, you're welcome!

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Thank you!