The only provider you'd learn coping mechanisms through is a therapist/psychologist/counselor, and they won't require a diagnosis. However, there's plenty of YouTube channels, books, websites, and other tools where you can learn a lot of those coping mechanisms you have have missed out on.
If you were talking about getting meds, you can sometimes just find proof of your original diagnosis, and that'll be enough for your current primary care doctor to medicate you.
If you were under the mistaken impression that you have to get a new diagnosis in order to be diagnosed with ADHD instead of ADD as an adult, you don't. The term "ADD" is simply defunct now as ADHD and ADD are now considered the same disorder with the hyperactivity in certain individuals sometimes manifesting and not in others. It's very similar to how the term "Asperger's syndrome" is obsolete because it's simply considered a manifestation of autism.
Why did you have to give away a dog? What made you able to get given a new one?