NOTE: Others in the Apple support forum linked below have reported that these steps do the trick for them. It does not seem to be working for me, however. How about for you?

Daily my MacBook gets a number (2), (3), or (4) added after its computer name. After running searches and culling through forums, I found a tip which seems to be working.

Apparently this can be cleared up by repairing disk permissions. Here are the recommended steps:

1. In System Preferences > Sharing, remove the (2) [or whatever is extra; mine was iMac (2), so I removed the (2)
2. Exit Preferences
3. Shutdown
4. Restart machine in Recovery mode (machine off, press and hold Command + R, power on, when Apple logo appears release keys) — may take a few minutes to boot (depends on machine generation/speed, RAM and such)
5. Open Disk Utility
6. Select the OS disk (mine was Macintosh HD; selected the ‘indented’ item)
7. Run Verify Disk Permissions
8. When finished run Repair Disk Permissions
9. Restart

Source: Apple Support Communities Discussion Here — in the Oct 29 reply by farquaad