It’s outside the purpose of a certificate for you (the subscriber) to convey arbitrary information. You can put that on the website or in your domain registration info (WHOIS/RDAP).
The information in a certificate is limited to what an issuer/CA can actually attest to.
I guess an analogy would be the situation with doctor’s notes - we don’t want a situation where you’re coming into work after an absence with something that says “patient reports that they feel too unwell to work”. 