I'll try to be as strict as I am on Lang-8 :) Even though, I don't like the correction interface on italki -- it's impossible to add example sentences and explanations.

Originally, China called our country "Yamato". Some references say that such word gave Japan scorn; however, I am not sure if it is true!

Eventually the Japanese changed the countries name from やまと to 日出処（ひいずるところ）.

* This would work better with the year. e.g. In the Xth century, the J... *

日出処 means 'the place of the sunrise' and 日出処 was translated as 日本.

日出処 may not have any relevance with 日本 for you, does it?

But... 日（ひ） means the sun. 出（いずる） means 'to go out = to rise'. 処 （ところ） means 'a place'. In addition to the meaning of 'book' 本 has a meaning of 'the start' or 'the beginning'.

* Being completely strict, you cannot use an ellipsis like that; however, many natives will use an ellipsis to convey the same meaning. See: http://thewritepractice.com/how-to-use-an-ellipsis-correctly/ *

The Chinese came to call our country 'Jippon' in their accent, but Marco Polo heard the word 'Zipangu' instead of 'Jippon'.

English speakers back then heard 'Japan' instead of 'Zipangu' in an English accent.

Then, that wordspread all over the world.

Does that make sense?? XD