How do I change profile name on Minecraft

If you're on Windows, you could have a batch file to run for each child.

Here's an example (for John):

@echo off
set APPDATA=%~dp0\John
set LAUNCHER=Minecraft.exe
%LAUNCHER%

This script will change the %APPDATA% variable to wherever your batch script is with the "John" directory within. This will create two separate instances of Minecraft all together, so not only worlds (saves) are separate, but the whole game (resource packs, Java binaries, etc). You would naturally change "John" to whatever your child's name is.

Hope this helped.

You can make two separate profiles on the new launcher, clcik the New Profile button.

This screen will appear.

If you don't know what to do on this screen, leave everything the way it is except for the name

You can edit either profile at any time by clicking the Edit Profile button.