My question: Firefox and Chrome both complain about a lack of ownership information and grump about it being unsafe. How do I add that to the SSL certificate?
The operating system my web server runs on is (include version):
linux 2.6.32-696.18.7.el6.x86_64 x86_64
My hosting provider, if applicable, is: Jumpline
I can login to a root shell on my machine (yes or no, or I don’t know): no.
I’m using a control panel to manage my site (no, or provide the name and version of the control panel):
Yes.
I can also log in to a shell, just not as root
The version of my client is (e.g. output of certbot --version or certbot-auto --version if you’re using Certbot):
certbot 0.36.0
Chrome is complaining about your TLS/SSL version and ciphersuites, which are part of your server configuration (https://ssl-config.mozilla.org/).
Your certificate is fine, but you need to update your Apache configuration to use a modern TLS/SSL version and modern ciphersuites.
However, your version of Apache is very old - Apache 2.0.52. It’s so old that it might be the case that it doesn’t actually support any modern TLS/SSL settings.
Since you don’t have root access, I think you might need to ask your web host about what upgrade paths they have available for you to get to a modern, secure configuration.