My two cents, for Japan:
Early Joumon-jidai (-2200 to -1200) name: Joumon, leaders: ?
Middle Joumon-jidai (-1200 to -800) name: Joumon, leaders: ?
Late Joumon-jidai (-800 to -250) name: Joumon, leaders: ?
Yayoi-jidai (-250 to 300 AD) name: Yamato, leaders: Jinmu-tennou (?) (technically he should be in -660, but he was not Joumon)
Koufun-jidai (300 AD to 600 AD) name: Yamato, leaders: ?
Nara-jidai (600 AD to 900 AD) name: Yamato, leaders: Shoumu-tennou (?)
Heian-jidai (900 AD to 1200 AD) name: Yamato, leaders: Fujiwara-no-Michinaga
Kamakura-jidai (1200 AD to 1450 AD) name: Nippon, leaders: Minamoto-no-Yoritomo, Ashikaga Takauji
Sengoku-jidai (1450 AD to 1550 AD) name: Nippon, leaders: ? (there wasn't a centralized Japanese government, and no one was really important)
Azuchi-Momoyama-jidai (1550 AD to 1650 AD) name: Nippon, leaders: Oda Nobunaga, Toyotomi Hideyoshi, Tokugawa Ieyasu
The rest of it really isn't interesting, thanks to isolationism, so the rest all fall into the 'Edo-jidai' category (which really starts in 1600, and lasts till 1868). If you want to simulate a lack of isolationism, that might require some creative thinking.
Flags:
Joumon (up to -250): something involving
this?
Up to 1650: probably
this
1650 to 1868:
This
(whenever 1868 falls would be the end, then you would use the modern Japanese flag)