It would seem to me like you should just tell your therapist. Isn't that why you're going to therapy... to work on coping with your mind?
How can this therapist help you if s/he doesn't know?
This begs further questions: Do you really want this therapist to try to help you? Do you trust that s/he is an advocate for you? An ally, not an enemy?
If the answer to these questions is 'No,' then you should not tell him/her. If the answer is 'Yes,' then you SHOULD.
It's not fair to ask someone for help, only to deny them the opportunity by withholding information. Totally understandable, given your anxiety about the situation, but still unfair to the therapist.
As to 'how [you're] supposed to say that,' I think you said it just fine. Very succinct. Any other words would just be padding and aren't necessary to get your point across. "I have Imaginary Friends." Once you get this out, I'm sure your therapist will seek further detail, at which point you can then worry about specifics. Blurting it out in this fashion may be the easiest, least painful method.
I'm sorry you're so lonely. You seem like a very nice, sensitive, self-conscious person. I already consider you to be a friend in spirit, having never met you. You are a fellow human being--confused, lonely, and in pain. You don't need to suffer alone, if you don't want to.
Yes, there are people who will judge you. There will always be such people. You know what I have to say about them? F___ 'Em. There are too many kind, understanding, patient, and gentle people to focus on the judgmental and the small-minded.
I wish you a very positive, constructive therapy session. I don't expect--nor would it be fair to expect--a Sea Change or some other massive, transformational shift. But I do hope you take a couple of small steps towards whatever it is you're seeking.
Best of luck and Regards.