If you buy a new Windows Phone/Windows 10 Mobile device (e.g. a Lumia 930 or 950) and you have already an other Windows Phone, probably you would like to restore the same configuration you had in that old device: in fact, this is one of the proposed options that you have while configuring the new device with a wizard.
It is very convenient to have a Wi-Fi connection (as fast as possible) when you do the following procedure.
First you have to force a backup on your old phone (Settings -> Backup) in order to have in the cloud the last configuration of that phone. Then on the new one select, during the wizard setup, the restore option of the restore from the old phone. The new phone will install all the app you have, configure the emails you have, compose the Start page with the same tiles you have on the old phone! … then it will take a while to download all the apps and may be you will be requested to insert a password for each email account, but at the end you will have the new phone with the same configuration of the old one, the same apps installed, the same tiles position in the Start screen, the same WiFi connections already configured with password (at least for some of them, but this surprise me anyway!) … BUT even in the name!! … and this last thing could be not nice! 😉
Between the lines, note that all backups of all your devices are in your OneDrive space and you can see them (and possibly delete some) from the OneDrive site going to Setting -> Options – Device Backup.
So, how to change the name assigned to the new phone?
If you have the new Lumia 950 with already preinstalled Windows 10 Mobile, it is very easy: just go to Settings -> System -> Information about and then click on the Modify name button.

Modify the device name in Windows 10 Mobile
If your new smartphone (e.g. Lumia 930) has instead still Windows Phone 8.1, once there was the Windows Phone app for desktop that allowed to handle a Windows Phone device (and, among other things, allowing to change its name, the one visible also when you try to get a Bluetooth pairing). Now, in Windows 10, there is the Phone Companion app (that is no more specific for handling a Windows Phone / Windows 10 Mobile but it can be used with whatever phone device – e.g. Android , iOS), a lot of features are (for now?) not available. Anyway most of them can be performed very easily in other ways: for example the renaming of the device.
The simple procedure (that must be used for Windows Phone 8.1 devices but can be used also, as an alternative, for Windows 10 Mobile ones) consists in opening File Explorer in your PC, connecting your Phone to that PC via USB, selecting This PC (note: on Device and drives section the Phone icon will appear) and then renaming its label (click, wait and change the label text: see the following animated gift).
Note that this simple procedure changes the name of the device also in the device itself, non only for that PC: in fact, if you then go to see on the phone the Settings -> Information, you will see that the name of the device has been changed; the same if you try to configure a Bluetooth connection, for example, with a PC.