How to assign a tag from a custom html form?

It’s not possible via a hidden field. You can do it with custom code though:

https://github.com/ibericode/mc4wp-snippets/blob/master/integrations/subscriber-tags.php

By changing the filter slug you can target it at a specific integration method:
https://github.com/ibericode/mc4wp-snippets/blob/master/integrations/integration-slugs.md

If you want to specify it per form you would need to add your own custom code for that.
Here is a code snippet example that would target specific CF7 forms:
https://github.com/ibericode/mc4wp-snippets/blob/master/integrations/contact-form-7/different-tag.php

Please consider getting the Premium add-on to our plugin. It will allow you to create unlimited forms and easily set tags per form and it also has a feature to email you and/or the subscriber directly after submitting the form just like a contact form would.

Hope that helps. If you have any questions, please let me know!