okay i was wondering if they were getting this figure from the "Prevalence" section of the DID section of the DSM-5 (p.294)
The 12-month prevalence of dissociative identity disorder among adults in a small U.S. community study was 1.5%. The prevalence across genders in that study was 1.6% for males and 1.4% for females.
which doesn't say anything about whether these people are diagnosed with DID, and also is about "a small US community study" in the last 12 months, not The Entire World.
But looking further, the NIH says "Approximately 1.5% of the population internationally has been diagnosed with dissociative identity disorder." which links to this article which is actually about testing some online program for patients but says "Dissociative disorders (DDs) have a reported lifetime prevalence of 9-18% in international general population studies, with the most severe DD, dissociative identity disorder (DID), present in approximately 1-1.5% of the general population" which links to an actual epidemiology of Dissociative Disorders from 2011 (DSM-IV era).
It looks at the prevalence of DID diagnosis in patients already in clinical settings (inpatient care mostly) from various European, Asian, and North American countries (crucially these are all countries that have a DID Diagnosis on the books and a robust enough psychiatric system to provide usable data), which actually varies wildy from 0.4% (swiss hospital) to 14% (turkish hospital). Now, for the general population, it uses a few studies where groups of people were given a Dissociative Disorders screening (DDIS or SCID-D) and reports the percentages of that population who were then diagnosed with any dissociative disorder and who were diagnosed with DID specifically. For DID, the numbers varied from 0.4-3.1%, with the 1.5 figure specifically coming from Johnson et al in a North America study.
So, yeah, it does seem like "In one study, 1.5% of a population was diagnosed with DID after being screened for dissociative disorders" got telephoned into "1.5% of people everywhere have a DID diagnosis"