iPad Pro 11-inch (3rd gen) does NOT connect to iMac 24 inch M1 with the USB-cable supplied with the iPad and does not show up in Finder

Not sure what you are referring to Apple is VERY clear in the Tech Specs (iMac 24-inch - Technical Specifications - Apple) where it clearly shows:

Also, please learn how to use SideCar. Apple explains this in Sidecar Whitepaper (apple.com)

[Edited by Moderator]

There seems to be several wrong assumptions on your part.

The name of the device does not come from Apple. You can change it to whatever you want in System Preferences->Sharing->Computer Name.

If it shows "MacBook Air" from there is probably because you restored a backup made from an MBA onto this Mac and it simply applied that name. The "(2)" part is automatically appended by the system to the name when it detects another device with the same name on the network. This is to avoid issues when more than one device is named the same.

The iPad should connect to one of the Mac's USB ports. What do you mean it does not? Why would that be a catch 22? Please explain the issue.

As has been pointed out Apple does clearly point out in the device's Tech specs how many screens it supports.

If you want help please explain exactly what issue you are having, and somebody can help you out