This isn't a very common problem but it occurs when a user it put into AD incorrectly, then SharePoint does its AD sync and the name is stored in the User Profile database with the wrong spelling. Later the name is updated in AD and SharePoint will sync the correct name. The problem is that for some reason the Option Menu display won't update to the correct spelling. That is unless you force it to, the following steps explain how to force the update and correct the issue.
1. Open the SharePoint 2010 server that hosts Central Admin
2. Click Start
3. Click All Programs
4. Click SharePoint 2010 Products
5. Click SharePoint 2010 Management Shell (run as administrator)
6. Type Set-SPUser -Identity 'Domain\UserName' -Web http://SharePointServer -SyncFromAD
7. Hit Enter (the script will run and once complete will prompt you that it completed)
Once the command completes you should be able to go back to any SharePoint page and the user name should now display properly. If it doesn't this could be a simple browser cache issue, so depending on your browser of choice clear cookies and cache and re-open SharePoint. The issue should now be resolved.
Well hopefully this fixed your issue with the SharePoint 2010 user name displaying incorrectly in the option menu. I know this can be a frustrating issue for users; they of course want their name displayer properly.
If you are unable to use the Exchange AD synch option described earlier, sign into SharePoint as as a different user and delete the wrong username. Open the option menu next to the username in the SharePoint page and choose "Sign in as a Different User" and sign in with a different user credential. Go back to the options menu and choose the "My Settings" option; the wrong user name should still be displayed on the sharepoint site. When the settings page open, click the "Edit Item" option. Within the edit window, choose the option to delete the username with the wrong information. Logout of the sharepoint page and then log back in with the right user credentials. This process should update to the correct user data on the sharepoint page.