Well, yes, though not exactly the way you're asking. In early exchanges with China, Chinese documents such as the Book of Han referred to Japan as (my Romanizations will come from the Japanese side of things here) Wa or Wakoku, written 倭/倭国. This carries certain negative connotations because of the component radicals that make up the character 倭, giving an impression of someone bent over/small in stature.

Japanese scholars soon realized this and began using the character 和 instead, which is pronounced the same in Japanese but means "harmony" or "peace" instead. This is where you get words like wagyu (和牛), Japanese-style beef.

Japan did a lot of this kind of subtle diplomacy back and forth over the centuries with China in their bid to avoid being a full vassal of the Chinese. Translations in Japanese sources such as the Nihon Shoki sometimes altered the Chinese characters used to be less submissive.

As such, your assertion that the current characters used for Japan are originally Chinese is more complicated that it seems from your statement. Sure, the characters themselves are originally Chinese, but it is disputed as to whether the first use of them to refer to Japan came from the Japanese side or the Chinese one. "Origin of the Sun" (日本) could of course refer to the sun rising in the east if you are in China, but it could also refer to Japan as the birthplace of the sun goddess Amaterasu. Sources are, as far as I'm aware, still divided.

This touches interestingly on a part of history that we all try to avoid as best as we can, which is that there are a lot of political pressures surrounding topics like this because of modern geopolitical considerations. China would love to have come up with Japan's name, and Japan would love them to have not. In this way things haven't changed all that much since Prince Shotoku sent a letter to the Chinese Emperor saying "The Son of Heaven in the land where the sun rises addresses a letter to the Son of Heaven in the land where the sun sets."