Kirk here with some thoughts about names for the place we currently call “Kumamoto.” Kumamoto is on the island of “Kyushu” (九州), which literally means “nine states.” However, the “states” (州) were actually called “countries” (国) and this place was called Higo no Kuni (written “肥後国”). So, what was “Kumamoto”? Well, in the Edo Period, different parts of Japan were governed by “han” (藩) or “domains” and “Kumamoto Han” was the name of the domain started by KATO Kiyomasa and later taken over by the Hosokawa family.
The Edo-period system is rather confusing because the domains (藩) are not synonomous with the countries (国). The following Wikipedia article says that the domains (e.g. “Kumamoto han”) were the “de facto” (that is, the actual) administrative units, while the countries (e.g. “Higo no kuni”) were the “de jure” (that is, nominal) adminstrative uints. https://en.wikipedia.org/wiki/Han_system
So, administration of countries (that is, places like Higo) could be split between a number of domains (han) that did the actual governing. In fact, the entire area of what is now Kumamoto Prefecture was not governed by the Kumamoto Domain in the Edo period. Before the Shimabara Rebellion (about 1637) it was governed by the Tomioka Han. (Footnote: Modern Tomioka-machi gets its name from this domain.) However, after the rebellion the Bakufu (central government) ruled over it directly, as it did over Nagasaki. (If you want something done right, do it yourself!)
This confusing han vs. kuni system was abolished soon after the Meiji Restoration when the current prefecture system was established. Hence, Kyushu now has seven prefectures, not nine, but the number 9 remains in the region name for historical reasons.
I’m not sure what conventions regarding the naming of han (domains) influenced Kato Kiyomasa but, for whatever reason, he choose a pre-existing place name (Kumamoto) rather than his own family name (Kato). But, as William has already pointed out, he changed the Chinese characters from 隈本 (orgin of a nook) to 熊本 (origin of a bear): https://www.facebook.com/Kumamotoi/posts/5437695429637178
Name selection can be very important important in marketing. Thanks to Kato Kiyomasa we have a cute bear mascot named “Kumamon,” not one called “Nooky.” ;)