This is an old issue. Despite numerous reports from users annoyed by it, it has not been fixed.
After each blog post, Drupal displays a link called "$user's blog", on both the front page and on each individual node page. This might be useful in some situations, but in other cases it's just annoying. There is no way to turn it off, other than patching the core.
Reproduce the bug:
Just post a few blog nodes.
I expected to be able to go to the Admin section and turn off the display of the "$user's blog" link.
Instead, there's no easy way to turn it off, other than hacking the core.
Some discussions and patches: