Q. What is the name of the therapy that requires patients to name objects in a room?

The therapy you are asking about is most likely Prolonged Exposure Therapy (PE or PET). Shia LeBouf, the director of 'Honeyboy' mentioned in an interview that PE helped him overcome childhood trauma. PE is strongly recommended by the American Psychological Association (APA) for the treatment of PTSD: https://www.apa.org/ptsd-guideline/treatments/prolonged-exposure.

Naming objects in a room is also an exercise used in EMDR therapy to help a patient decrease feelings of dissociation.