Site-wide SSL is not satisfactory

[ForumJoiner]

My web host's name is xxx.com
My site's name is yyy.com, and my site is hosted on xxx.com.
The real address is yyy.com = home/yyy/public_html

Now, my web host recently installed SSL certificates, site-wide.
When I access yyy.com, IE complains that the name yyy.com does not match the name xxx.com.

Someone told me that my server maybe uses "shared SSL".

What can be done in this case?

 

[temi]

ForumJoiner, SSL is usually installed for a domain, which has to be hosted on a dedicated IP address and not a shared IP address. If you do that you SSL certificate would work fine.
Did you request that an SSL is installed for you domain or your hosting company just offer you a free SSL?

 

[ForumJoiner]

It looks to me that the web host solved almost all the problems. Right now, the only problem is that the host put my domain's name on both "Issued to" and "Issued by" categories and the IE complains about that. I hope they will fix it soon.