imac renamed by network

You can't have the same +Computer Name+ for two Macs on the same network.

Change it to something meaningful, via +System Preferences > Sharing.+

For best results, keep it relatively short, and use only letters and numbers (no punctuation).

macsync wrote:
I get a message on screen saying that another mac on my network has the same name so it changes the name by adding a number so my imac is now called imac5 any idear why

If you only have one iMac, then some Mac software quirk is causing its software to think there's already a like-named Mac on your network. As Pondini suggests, you can rename it, but that won't guarantee that it will be renamed again in the future. I had such a problem a long time ago (perhaps with OS X 10.4). I lived with it until it went away after I upgraded to the next major OS X release.

By the way, if (as suggested by your system details) you're really running OS X 10.5.2, unless you have a good reason to stay with that, you should consider installing the free updater to 10.5.8 ( http://support.apple.com/kb/DL866). There's a slight chance it will fix that renaming problem.