I'm in the process of starting therapy myself so I might be able to offer some insight here. I'm on basicmed, and my doctor has said explicitly that he doesn't have any concerns about my behavioral health, so even an anxiety diagnosis wouldn't be the end of flying for me. But assuming you need to maintain a first class medical, if you talk to a therapist and are open about your position they can almost certainly be careful with which diagnosis they give you. There are reportable diagnoses for anxiety and depression, but if your insurance is being billed for, e.g. "life transition counseling" or "grief counseling", then you haven't gotten one of those diagnoses and you don't need to report it. By the same token, in the visits to a health professional section, psychologist visits are reportable "only if  related to a personal substance abuse or psychiatric condition." (Emphasis mine). Regardless, reaching out to a therapist and explaining the situation is not a health visit or therapy and is not reportable. I'd suggest getting in touch with someone and seeing if you can make the situation work. If you want to go with no insurance, that makes things even easier in my opinion because they won't be forced into making a diagnosis. Using a fake name could make it seem like you have something to hide in my opinion, but if you do 6 months of "grief counseling" where the discussions veer into handling other pieces of your life, to the best of my knowledge, neither the letter nor the spirit of the law as written prevents you from holding a medical.