I recently upgraded my iPhone 5c to an SE. Everything seems a little smoother on the SE (although I’d swear blind it gave me an electrical shock while scanning my fingerprint!).
When I upgraded, so that I didn’t lose anything, I simply restored the latest backup from the iCloud account linked to the 5C. However, when I got on the train and tried tethering my laptop to the phone, it failed. In fact, it looked like the WiFi connection to the phone was actually broken, as it kept flashing connected and would then disconnect!
The fix for this turned out to be relatively straightforward, you simply rename the phone:
Settings -> General -> About -> Name
And give it a different name than the previous phone.