I don't have a specific nickname for my T, but I do have a euphemism for "therapist", a common noun that means something completely different in normal speech, which I use with two of my friends. So I can mention off-handedly that "I saw my visitor today" (if the word was visitor, which it isn't), or ask the friend who is also in therapy "Have you talked to your visitor recently?" - and when you're out in public, that is really useful. Because a word like "therapist" just might be overheard by somebody you don't want to know, but you can bandy "visitor" about and actually have conversations about therapy without anybody being the wiser.