Look, I know how I set it up. I set for blog.domain.com and the http://www.name.com was pointing to the domain's own site.
It was not the DNS settings, as I tried it on multiple domains, same issue.
Also, why would anyone set up a www for a subdomain? Like said, the domain and www were set to where the domain was added, in cPanel, to it's own site. I tried to set blog.domain.com to point to the blog for that site, on my multisite setup on another domain.
Now, I had thought, maybe it was due to both domains being active on same cPanel account, but then tried another domain, on another account, and same thing. Whenever I set blog.name.com it open and redirects to http://www.blog.name.com