Yes you can change your kids diapers in public and it will become necessary to change a kids diaper when in public because you can't let the kid stay in a wet or dirty diaper too long.
If possible take the kid to a bathroom or restroom where there are changing tables and put the child up on the changing table and change their diaper in there to be as discrete as possible.
Sometimes you may need to change the kids diaper out in public on the ground such as at a big event etc and if so you should try to cover the child's private areas with a towel or something to block the view of any potential onlookers.
Try to make the diaper change in public as quick as possible to avoid leaving the child's private areas exposed for too long.
Or if possible take the child to the car or other vehicle and change the child's diaper there out of public view.