Adding alias domains with SSL to my website

I recently registered a new domain that I’d like to add as an alias to my website. I’ve added the new domain to my project but I’m a little confused as to how to configure it as an alias.

I added a CNAME record for the new domain that points to the current domain, as per this article. However, when I access the new domain, my browser returns an “ERR_CERT_COMMON_NAME_INVALID” error. I assume this means that a valid SSL certificate needs to be added for the new domain.

Does this mean that I need to add a Let’s Encrypt SSL certificate for the new domain, like I did for the old one when I created the site? Or do I replace the site’s existing Let’s Encrypt certificate with a brand new one that includes both domains?

FWIW, my droplet is running Ubuntu 20.04 and uses Apache.