What type of webform are you using? The Pipedrive Webforms don't currently support adding labels.
For other webforms, it would depend on how they're built out as our API does allow for adding Labels: https://pipedrive.readme.io/docs/working-with-labels
I was looking for this answer too and a bit annoying it cannot be added via a webform of the chat bot.
However that being said I have created a work around using the automations and the title prefix.
Basically in the prefix add the source i.e. webform, then create a trigger saying when a deal created containing the prefix name add the label 'website'
Only downside is the deal title contains the prefix which I want to remove.
To add to this, add a second trigger saying update field, deal title and chose contact name and you remove the prefix.