External SSD in iMac

What are you going to use the SSD for?

If you are just going to use it for storage, then you will just need to format it.

If you are going to use it as a startup disk, then you need to format it, install macOS on it and then migrate from your Internal Drive or Time Machine during the initial setup.

The external SSD will be named what-ever you name it, when you format it for your Mac.

I would suggest placing that external SSD in a USB3.1 gen 1, or gen 2 enclosure. Connect it to your Mac with either a USB3 gen 1 cable, or USB-C cable if provided with the enclosure, to ensure maximum throughput. Placing the SSD in an available USB2 enclosure would be counter-productive.

Externals do not show up in the "Storage" section of Desktop, but as separate drives: