Delusional belief about subjective double is called:
Doppelganger is the delusional belief that there is a subjective double. Delusion of misidentification are of two types - positive and negative. Negative misidentification is called as Capgras syndrome. Positive misidentification is called as Fregoli's syndrome. Autoscopy is looking oneself externally and knowing it as themselves.
Doppelganger
Autoscopy
Delusion of misidentification
Depersonalization
Schizophrenia Spectrum and Other Psychotic Disorders