In the U.S., if they decide not to work with you anymore, I think they have an ethical obligation (by the standards of practice) to give you a referral. I think if it is the client who is quitting therapy, the same obligation does not apply, but if the client asks, the therapist may be able to supply names.

A few years ago I told my T that I wanted to do family therapy with my daughter. T told me he could not provide that (even though he is a family counselor), and he helped me find someone who could. He gave me the names of several people he knew, helped me research them online, etc. My daughter and I ended up going to one of his referrals and it worked out well.