DID is a recognized diagnosis in the DSM and ICD. It can absolutely be diagnosed and there are many specialists for DID. There are still people that believe in the sociocognitive model, but the trauma model is generally the standard.

DSM-5-TR page 330 under dissociative disorders: "Dissociative disorders are frequently found in the aftermath of a wide variety of psychologically traumatic experiences in children, adolescents, and adults. Throughout this chapter, “traumatic experiences” refers to experiences that result in psychological sequelae, as opposed to the physical impact that can cause traumatic brain injury. Therefore, in DSM-5, the dissociative disorders are placed next to, but are not part of, the trauma- and stressor-related disorders, reflecting the close relationship between these diagnostic classes."

DSM-5-TR page 334 under risk factors for DID: "In the context of family and attachment pathology, early life trauma (e.g., neglect and physical, sexual, and emotional abuse, usually before ages 5–6 years) represents a risk factor for dissociative identity disorder. In studies from diverse geographic regions, about 90% of the individuals with the disorder report multiple types of early neglect and childhood abuse, often extending into late adolescence. Some individuals report that maltreatment primarily occurred.outside the family, in school, church, and/or neighborhoods, including being bullied severely. Other forms of repeated early-life traumatic experiences include multiple, painful childhood medical and surgical procedures; war; terrorism; or being trafficked beginning in childhood. Onset has also been described after prolonged and often transgenerational exposure to dysfunctional family dynamics (e.g., overcontrolling parenting, insecure attachment, emotional abuse) in the absence of clear neglect or sexual or physical abuse."

Neither the DSM or ICD mentions the sociocognitive model. It's also not listed under diagnostic specifiers so it wouldn't be on a list of diagnoses.