When I was looking for a therapist for my daughter, I talked to my friends for recommendations, and she talked to her friends for recommendations. It is so incredibly common these days for teens to go to therapy. This might help your daughter be more receptive if she knows someone who has seen the same person.
Even with that, we went through 3 therapists before finding one my daughter wanted to stick with. This is also extremely common. I think conversations with your daughter normalizing the situation might help.