This is one of those hats that I'm having trouble categorising as it was donated, its origin was as a gift to a friend visiting Japan, however, the hat is not Japanese.
The hat is well made with a tapestry pattern on display.
Inside the hat is a label which google translate fails to recognise, so not sure of the language, something Asian.
This hat is too rigid to be a comfortable Leisure cap, its similar in some ways to Birretta, mostly its unique, at least to me.
NEW 3rd October 2020 - Finally found what I believe this hat to be, its called an Uzbek Duppi Cap or Uzbek Doppa cap