"People's Republic of" vs "Republic of"

I saw someone from "Republic of Korea" visited my website , and thought it was from North Korea. I became very excited, thinking that wow, people from North Korea actually visited my website?
However, upon second thought, I realized "Republic of Korea" is South Korea, North Korea is "People's Republic of Korea".
This reminds me of another incident. When I went to the post office to post Shen Yun Calendar  to Taiwan, upon seeing that the address ended with "ROC", the staff member asked me, "What is 'ROC'?" 
I told her that it was "Republic of China", and that Mainland China was "People's Republic of China". So please don't get it wrong.
How confusing, isn't it? And how ironic that countries with "People's" in their names are actually caring least about their peoples!