Correct, It looks like you are using the default certificate. To fix it, you will need to purchase a certificate from a Certificate Authority like Verisign.
In not any case you will buy a certificate to get this warning message fixed.
In a domain environment you can easy use the internal certificate (customized with your data) of the MEG.
Deploy the certificate via Group Policy.
Chrome uses the same certificate database like the IE.
A little bit different are Firefox, but also there is a workaround, we use.
This is what we use, to deploy the certificates for firefox without overwrite existing certificates at the user profiles.
I know it is not exat what you asked, but maybe helpful for others.