No free service I know of will let you generate a certificate on the fly with your name on it, which will be considered trusted by most out of the box sw

You can get free digital certificates to sign PDFs with your email address, from basically any company. But that is hardly a way to verify your identity. Anyone can create any email address they want, and use any name in the address.

The eIDAS directory lists some companies that are pretty cheap. But you will still have to verify your identity, so you can't get a certificate as easily as with Let's Encrypt for websites.

Edit : Docusign and similar services have a free plan, but you can only sign a few documents before you or the submitter have to pay. So it's not free per se, it just has a trial. And they don't really check your id, most of the time. So anyone can create an account with your name too.