There might be several possible reasons why you get this error when you try to access your web site:
If a certificate was issued by a trusted Certificate Authority, you will see the name of the Certificate Authority in the «Issued By» section.
If the certificate is self-signed, it will contain your company name/your web hosting provider company name/your server name, etc (see fig. 2). You will need to remove a self-signed certificate from the server and install the one issued by the Certificate Authority.
Note, when removing a self-signed SSL, please make sure to save the private key, since it will be required for the SSL installation.
Note, if your server supports SNI technology, you will not need a dedicated IP address for every certificate installed on the server. You need to discuss this with your hosting provider.
Below the information about the certificate you will see the Certificate Chain section which will inform you if a full chain was installed. To make sure you are installing Bundle files in a correct order (unless you have the certificate in the PKCS#7 format)
Note, this is only possible, if you have full root access. You may only set one SSL Certificate for services; it must be used for the server name.
If you are installing a certificate using OpenSSL or ModSSL on Apache, you may need to comment virtual hosts for the certificate to start working properly after the installation. If you are not sure on how to do this, please ask your hosting company to do this for you.