https://blogs.msdn.microsoft.com/benjaminperkins/2013/02/01/adding-a-hostname-to-your-ssl-certificate-binding-on-port-443/
In particular a reader comment about setting the host name:
That * doesn’t mean that is wild card certificate necessarily.
In IIS7 (on Windows 2008 R2), I saw missing hostname under ‘Edit Site Binding’ [your first screenshot]. That was the first SSL 443 website on that IIS server. The website was dynamicsSharePoint.domain.com and I used internal certificate server to issue the certificate for that internal Dev / Test site.
- I resolved the missing Hostname by opening the MMC console on the server and adding Certificate MMC for Computer
- Expand Personal node under Certificates (Local Computer) on server
- Right click on the certificate in the list and choose properties
- Under General tab, change the ‘Friendly Name’ from dynamicsSharePoint.domain.com to *.domain.com and click OK
- Go to IIS Binding for the website and you should be able to add Hostname and pick the *.domain.com certificate.
- Verify the website and you will see certificate in browser with the FQDN / dynamicsSharePoint.domain.com