I need to identify a name of an iPhone authentication function
Yes, the function is included in iOS 11 and is called "Automatic Setup".

It is designed to get you up and running quickly when you replace your phone with a new one. Essentially you power up the new, blank device - then place your old phone near the new one. A popup will ask you if you want to use Automatic Setup.

Then the animation you refer to will be shown on the new device, which you then scan with the camera on the old device.

After entering your old pass code the data from your old phone will be transferred to the new phone.