There is NO "registry".
You must be DISABLED to have a service dog. Having autism or otyer issues doesnt necessarily qualify you as disabled. The dog has to be trained to perform tasks to mitigate the disability (comfort, calming you or making you feel safe/calm are NOT service dog tasks) the dog must be able to perform in public, without being distracted, without showing ANY form of aggression, begging for food or attention, being disruptive, or unhousebroken.
Emotional support animals require a note from the Dr who is treating you. They are NOT service dogs, not allowef in public. Only fair housing laws and airline access laws cover them.. Both with restrictions or exclusions. You need to request reasonable accomodation and get permission before moving the dog into a rental or onto an airplane. You cant just show up with papers you purchased online and expect entitlement.