Service animals (which under ADA means dogs) are protected by law as far as being permitted in public places with some sensible restrictions such as not allowed in food prep areas. They are not the same as so called emotional support animals. A service animal to meet the legal criteria must actually be trained to assist the disabled person.
I’ve encountered blind people with seeing eye dogs and you can always tell by the harness they wear.
Plus the dogs are EXTREMELY well behaved. They are highly trained when when wearing the harness are on duty as trained. The dog’s focus is on doing his job.
OK..
How does the establishment know if the animal is real or fake?
You are not permitted to ask.