Back in the old country (Pakistan), persimmons are called جاپانی پھل /jaapaani phal/ or « Japanese fruit ». Are the fruits really Japanese?
The Asian or Japanese persimmon is certainly widely cultivated in Japan, but no English-speaker would call it "Japanese fruit".
They are, their name for them is kaki. Most of those sold in GB are from Spain or South Africa, depending on the time of year.