Using a flash drive with iMac

I have a new iMac and an old eMac. I want to bring some files from the eMac using a flash drive. When I connect the drive to a usb port on the iMac, nothing happens. The iMac doesn't seem to 'see' it. When I connect a flash drive to the eMac, it shows up on the desktop as 'no name' and I can open it, read files, drag material into it. How does this hardware work on an iMac?

On the iMac, if you open Disk Utility (Applications => Utilities) with the drive plugged in, does it appear in the list of drives?

Thank you for replying. I accidentally discovered how to solve the problem. I removed the flash drive, since it seemed not to be functioning, and a message appeared on the desktop telling me to drag the icon to the trash before removing it. It also said I could select the accessory drive in Finder. I put the drive back in place and went to Finder. No sign of it. I noticed Finder Preferences and clicked on that. One option it gave me was to have the Hard Disk, or an accessory Disk show on the desktop. After I chose those, the icon appeared and I could use it as I had with the eMac.

So many little details to discover in a new computer!

Nice bit of detective work. It's easy for experienced users to forget that setting. We set it once and forget about it until someone asks. Glad you got things sorted out.