Are you talking about the mood icon that appears next to the name. That shows you are online or offline?
If you are ,I guess there are a few ways to address that.
One would be to edit the template file and delete it completely.
You could edit the template, or delete the acronym in the language file, or just upload the mood graphic with a blank one.
For deleting completely.
There are two templates depending on how you display the author.
post_side.tpl
post_top.tpl
Control Panel » Templates » Template Editor
Select the file in question above.
Look for the section that starts with online_status and comment it out or delete it.
I would suggest to comment it out.
