Hi, and welcome to the forum! Just to clarify, there is no "official badge" that you need.
On the Camino, you are simply walking across Spain. Anybody can do it (if they are legally in the country, of course).
If you want to stay in special pilgrim albergues (run by municipal governments, churches, volunteer associations, etc) that are intended only for pilgrims, you need to show an official "credencial" (aka pilgrim passport) that is available from the Cndn pilgrim society, or from the Forum Store, or from many places on the Camino itself. If you want to get a compostella (certificate from the cathedral) in Santiago and you have met the requirements, you need to show your credencial with 2 daily stamps (sellos) for the last 100 km you walked into Santiago.
Many people wear a shell on their backpack, but many don't. There is no requirements. (Some people argue that the shell was traditionally obtain in Galicia and then worn on the homeward walk.)
There is no overall registration system for pilgrims. Your name and information will be collected at various albergues and hostales to meet Spanish requirements for registering guests in lodgings and hotels.