When you mount a local hard drive in OS X it will appear in the Computer Name section of the Finder, but may also be found on the Desktop or in the Finder sidebar (unless you have disabled those options). Sometimes, however, when you attach a local hard drive, you will see that the name of the drive has a "-1" or another number appended to it. For instance, if you have a USB flash drive labeled "USB Drive," it may appear as "USB Drive-1" on your system.
In OS X, drives are accessed through the Finder's various locations, but on the filesystem they are given a mount point. The drive is first recognized and assigned a unique device ID (such as "disk1"--you can see these and other hardware device files by opening the Terminal and entering the command "ls /dev") and then is handled by the disk arbitration daemon, which identifies it and an available filesystem on it, and proceeds with mounting it if the system can recognize it.
The mount point for local drives is in the /Volumes folder, which is a hidden directory on the main boot drive. In this directory a folder is created and given the drive's name, and is used as the access point for all files on that local filesystem. If by chance you mount two drives of the same name, because the system can't create two mount points with the same name it appends sequential numbers to new mount points as they are created, and therefore you will see the numbered drive names in the Finder.
While the numbered names for disks should only happen if there are multiple drives attached with the same name, it can happen for other reasons as well.
When you eject a drive, the system should remove the mount point for the drive; however, sometimes this doesn't happen. Crashes or other improper ejecting of drives can sometimes cause the system to leave the drive's mount point in the hidden /Volumes directory, and then when you attach the drive again the system recognizes an existing mount point of the same name and will append a number to the new mount point.
To clear this problem, unmount all drives and go to the hidden /Volumes directory by entering the text "/Volumes" in the Finder's Go to Folder option (available in the Go menu). This should open the mount points directory, and if you see any folders, aliases, or other files in the directory that have the same name as your external drive, then remove them.
Use of multiple drives of the same name without rebooting
If you have multiple hard drives of the same name then the system will append a number to the end of each if they are mounted at the same time. If you then unmount the main drive, all other drives will keep their new numbered names, and will continue to do so regardless of whether they are ejected and remounted, until the system is rebooted. This is because the system associates the mount point name with the drive device (for example, "disk1"), which is then kept associated with a particular device for the remainder of the boot session.
To fix this problem, just reboot the computer and the drive's name should revert back to having no number.
If drive name problems keep happening, you might consider running a Apple Support Web site to see if that clears it up.on the system to clear and rebuild system caches and other temporary items and settings that might be contributing to the problem. At the very worst a reinstallation of OS X would take care of it, but even though this is a relatively easy thing to do with Snow Leopard, first try downloading and applying the latest Combo updater for your version of OS X from the