Our Colorado Animal Attorneys often see people who have ESAs with a certificate they got from the Internet. This is the greatest scam in the world, in our opinion, but that is another story for another day.
If your ESA is not trained to perform specific tasks related to your disability, then your dog is not an ESA. An ESA is an animal who is trained to perform specific tasks related to your emotional disability. An animal who makes you feel calm or better just by virtue of the animal's presence in your life is not enough to qualify your animal as an ESA.
That said, it is fairly straight forward to train your ESA yourself and therefore qualify your dog as an ESA. Under the FHA (which is the primary law that impacts ESAs, not the ADA) It is not required that your dog be formally trained by a company or professional trainer. The important thing is to make sure your dog is trained to respond to a specific symptom of your disability.
Despite what a lot of people say, if you represent your animal as an ESA but it is not, it's not a violation of C.R.S. § 18-13-107.7 because that statute only applies to intentional misrepresentations of a service animal. An ESA is not a service animal and therefore is not defined (or protected) under the ADA.