I seem to remember being able to make this work in the old app, but I cannot locate a place to change the name of a Thing in the new app on iOS. I feel like I’ve wandered everywhere, but would be happy to learn I just can’t see what is right in front of me.
It’s one of those “context-sensitive” menus.
One) choose rooms view
Two) choose things
Three) scroll down until you find the device you want to change. Now tap on the name of it, not on the control button
Four) now you are on the device detail screen. Click on the three vertical dots in the top right corner and you will see an option to “edit device” tap on that.
- now you will see the screen where you can change the device name.
I assume the latest software V 2.2.2 (1355) changed as this isn’t an option on my screen any longer. And I know a newer version is due for release any time. My only options are Name Change and temp offset.
I’m on the latest software also. You can still change the icon for lightbulbs and switches and some other devices.
However, it will not let you change the icon for a sensor. Apparently they only want you to use the official icons for those.
Sensor
Lightbulb
That appears to be correct. It’s odd that I have 2 garage doors, one’s icon is changed, the other I now cannot change to match it. I’m very frustrated today at ST as I had to change batteries in an open/close multi sensor that is used on the garage door so I know if it is open or closed. Assigning it to a garage door doesn’t appear to be an option any longer, and I can’t change the icon either. It’s as though it worked yesterday, but after changing batteries it now must be replaced because it is about 18-24 months old and software will not allow it to work as it did yesterday - on the same software. (HomeKit is looking better and better sometimes.)
I would report it as a bug to support just in case it’s a glitch that snuck in when they were adding the battery level reporting. Although, come to think of it, that might be why they’re locking the icons down, to support the battery reporting feature.
I don’t have a plug in sensor to check with but if somebody does it would be interesting to know if its icon can still be changed.
(As for HomeKit, I use it and like it, it’s just that it does much less than SmartThings and with a much smaller device choice. But it’s as close to a “set and forget” system as I’ve found. 
)
I have two lamps that are on plug adapters for ST and the icons there show they can be changed.