Pino,
What Richard described is a Astringent Kaki. It could be cold hardy relative to other Kaki, but Richards zone 8 location is not a good hardiness test. In general several of the ones normally considered more hardy are astringent, but that might just because there are many more astringent than non-astringent cultivars.
Richard,
Do you have a photo of the fruit, that might give us some likely suspects of cultivar. Some are identifiable. Like if they have a indented ring that kind of looks like acorn cap would likely Tamopan, Some cultivars were planted much more than others in past.