You're looking at the wrong spot in your Devices list. You need to look under "P." If you have both a device name and a device label set, the device label will be used as the display name, which is the larger text on the Devices page you show in your second screenshot. (The device name is there too in smaller text inside parentheses after it, though there aren't a lot of other places you'll normally see it--unless you don't have a device label set, in which case the device name is used as the display name and it's all you'll see.)
This is also not a problem. You can have as many devices with the same name or label as you want. That number is probably one at most, but there's nothing stopping you from doing otherwise. It's up to you how you want things to display. (Internally, devices are tracked by a database-assigned ID, so that's how the platform tells the difference.)