Do I need a separate ssl certificate for each domain that is pointing to my VPS server's static IP address?

VPS: running Ubuntu linux, accessed remotely via ssh. I have a single ssl certificate, generated using Let's Encrypt. All is working fine. This was before I added another domain, which is now also pointing, via DNS/nameservice, to this same VPS server's ip address. Do I need to generate a separate ssl certificate for each domain-name? I plan to have 2 separate websites, 1 for each domain name. And also a mail server that services both/each domain name's email requirements. Presumably I don't need separate certificates for mail servers and web servers, just the separate domains, if that.