The sign-off is a simple line at the end of the explanation for the patch, which certifies that you wrote it or otherwise have the right to pass it on as an open-source patch. The rules are pretty simple: if you can certify the below (from developercertificate.org):
Developer's Certificate of Origin 1.1
By making a contribution to this project, I certify that:
(a) The contribution was created in whole or in part by me and I have the right to submit it under the open source license indicated in the file; or
(b) The contribution is based upon previous work that, to the best of my knowledge, is covered under an appropriate open source license and I have the right under that license to submit that work with modifications, whether created in whole or in part by me, under the same open source license (unless I am permitted to submit under a different license), as indicated in the file; or
(c) The contribution was provided directly to me by some other person who certified (a), (b) or (c) and I have not modified it.
(d) I understand and agree that this project and the contribution are public and that a record of the contribution (including all personal information I submit with it, including my sign-off) is maintained indefinitely and may be redistributed consistent with this project or the open source license(s) involved.
The DCO requires a sign-off message in the following format appear on each commit in the pull request:
Signed-off-by: Random J Developer random@developer.example.org
using your real name (sorry, no pseudonyms or anonymous contributions.)
The DCO text can either be manually added to your commit body, or you can add either -s or --signoff to your usual git commit commands. If you forget to add the sign-off you can also amend a previous commit with the sign-off by running git commit --amend -s. If you've pushed your changes to Github already you'll need to force push your branch after this with *git push -f.
If it is really no option for you to disclose your real name and email address, there might be a chance that you can get your contribution accepted. In this case please contact the maintainers directly and verify the adherence to the DCO of the contribution manually. This might include quite some legal overhead for both parties.