I just tested this in my lab. I changed the name, and the certificate was the same. I set the time zone correctly (I had the default one at first), there was a new security exception, and I accepted the certificate. I checked the details, and it was issued today.
So the answer is; the modular server will generate a new certificate once a year, or when the timezone changes.
If you changed just the name, and a new certificate was not generated, try going in and changing the time (forward or backward by a minute, to be non-disruptive), and let us know if a new certificate is generated, and can be added as an exception in the browser.