Should a child call a counselor/therapist by first name or other?

I think she is probably afraid that someone will control her mind and she sees these exercises as a way for someone to get the foot in the door. These feelings are something the counselor has to work on. Compliance with instructions is a common problem in therapy and usually the reason for either sopping therapy or its general failure. Your daughter is acting fairly normally in this respect and it is probably one of the reasons she needs therapy: she knows what she has to do to make things better, she just refuses to do it because she wants her own way. Getting better usually means a person has to learn cooperation and to anticipate what others are looking for and negotiating so that everyone's needs are met.