Trusted public CAs like Let’s Encrypt are only allowed to write Fully Qualified Domain Names (or IP addresses) as Common Names for TLS certificates. It is not possible to specify something else.
But I think you will run into other problems sooner. The modern Web uses a technique called Server Name Indication, SNI, to have clients tell a web server what name they expect to connect to, and thus which certificate they expect, but the clients don’t provide any other details, just the name, so you can’t choose a different certificate for any reason other than the Host name of the web server the client is connecting to.
Are you sure your research project isn’t looking for client certificates rather than server ones? Both sides in a TLS connection may have a certificate. On the public web usually we don’t have client certificates, just server ones. But instead of clumsy usernames + passwords, it is possible to use a client certificate to prove your identity, and this is especially useful for web services, as opposed to systems used by humans directly.
Let’s Encrypt doesn’t specifically offer client certificates, although its certs can be used that way in a pinch. However you can make your own certificates, just for one particular service, which will often be suitable. You should look for documentation about making and managing your own client TLS certificates, perhaps with the openssl command line tools. Going into much depth is really beyond the purpose of this discussion site.