OK it looks like the issue you noted is the drives name which you can alter by just clicking on the name field like you change a file or folder. So I suspect you used another system to setup the drive which is why you see external in the name.
But we have a second bigger issue here! And that's the OS you used macOS 12.4 Monterey! Your system really can't use it which is why its deathly slow! The highest version Apple supports on your system is macOS 10.13.6 High Sierra
Here's the specs for your system 21.5" iMac Core 2 Duo (Late 2009)
As you can see at the bottom of the writeup: Pre-Installed MacOS: - Maximum MacOS: 10.13.x
Using your other Mac you'll need to setup a bootable OS installer drive with the proper version of OS. Go here How to get old versions of macOS to snag the correct version. Then using your other system get a USB Thumb drive (32GB) using Disk Utility reformat it to GUID and a journaled file system (HFS+ file system) then follow this guide How to create a bootable installer for macOS
Now plug in the Thumb drive into your 2009 system and reboot, you'll need to use the Start up command Option (⌥) so you can select the USB Thumb drive as the booting drive
Reference: Mac startup key combinations
You'll need to reformat your internal drive as its running the wrong file system (APFS) for this which needs macOS version (HFS+) using the USB Thumb drives Disk Utility. Then using the installer install High Sierra.