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.
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What is the make and model of the SSD you are trying to install?
crwdns2934271:0crwdnd2934271:0 Dan crwdne2934271:0
Samsung Electronics 870 EVO 500GB 2.5 Inch SATA III Internal SSD (MZ-77E500B/AM)
crwdns2934271:0crwdnd2934271:0 maylin crwdne2934271:0
OK, that's the right drive for your system.
FYI Your system offers a SATA II (3.0Gb/s) port, many people put in the wrong drive which is too fast. The Samsung drive is one of the few which is able to automatically match the systems port I/O which is why it is the correct drive!
So I guess the next issue is is the drives name the issue of the fact the new drive its self is not booting up? And what is the OS version you are trying to install?
crwdns2934271:0crwdnd2934271:0 Dan crwdne2934271:0
Ok,,, let me tell you ( i’m new at all this) lol
I already installed Monterrey on the SSD,
The SSD is already installed inside the imac (I remove the old hard drive and installed the ssd)
everything is operating (SLOW) but is working, I can go to Internet and do search , I can download applications etccc.. The only problem is that when I start up the computer it shows the ssd as external hard drive 😳. Let me see if I can post a short video.
crwdns2934271:0crwdnd2934271:0 maylin crwdne2934271:0
Did you swap out the HDD for the SSD or add the SSD to your system?
DO you see two drives on your desktop? Thats a good clue.
crwdns2934271:0crwdnd2934271:0 Dan crwdne2934271:0
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