You do indeed need a diagnosis for insurance to cover your sessions in the U.S. Some therapists use a diagnosis that's sort of generic (I think it's like "adjustment disorder") if they don't want to disclose something more specific to insurance.

My T and I have talked about my diagnoses because I came into therapy knowing what they were (long-standing depression/anxiety). She doesn't treat me like my mental health issues define me or anything, but it's helpful to talk about what's symptoms and what's "me."

Knowing the diagnoses also helps me find books and resources to learn more and get new ideas about what might help me feel better. I don't think labels are all bad, necessarily. But I admit that my diagnoses are not as socially stigmatized as some others.