Have Okinawans changed their names to Japanese names during the Ryukyu annexation?

I was exploring my lineage and reading documents, all names and last names were distinctively Okinawan, until I discovered someone in my direct lineage named Shuhei Nakaya. According to my general research, Shuhei is much more common in mainland Japan, but I know Okinawans adopted Japanese names or readings of their own names upon annexation, so it wouldn't be improbable to name your child in a Japanese way to avoid discrimination, but what strikes me is that the last name Nakaya apparently isn't at all common around Okinawa according to Myoji Yurai, as all of the kanji writings point to mainland Japan.

Does anyone have any idea if the name can be found with some ease in Okinawa? From what my dad knows, we're all Okinawans. Any ideas? Thank you in advance! Also, sorry to bother with a personal story.