It is showing you what it thinks is two computers - that happen to be named the same.
Go to "My Computers" and delete the one that you don't want anymore.

Each computer on the account shows up as one row on the "My Computers" page.
The delete option is on the far right on each row of info.
If you happen to only have one row of info on that page - just delete it and run a manual backup.
Edit: thx for the screenshot - it was very helpful.
Sig::: Practice restoring a file before you need a file in an emergency.
Using MozyHome (free) 2.20.2.276 on W7 Pro
http://mozy.com/home/download (file and release notes)
http://mozy.com/pro/download (file and release notes)