Example:
USA 美国 - 美 mean “beautiful” and 国 is “country”
So when my mom told me we were going to move to 美国, I, having never heard of anything about this country ever before, already had a positive impression of this “beautiful country”.
France 法国 - 法 is one of the characters in 法律, law, so my first impression was, that these people probably have very strict rules and are law abiders
Britain/UK 英国 - 英 is one of the characters in 英雄, hero, so I just imagine British people like to help the innocent (this was before I learned about British colonialism lol, but I guess the 英 character still sort of partly relevent, as in they view themselves as “hero”, aka: they interfere with other’s countries bussiness a lot)
Germany 德国 - 德 is one of the characters in 道德, morality, so I had a subconcious belief they were very moral people. I didn’t even know about the holocaust yet. 💀
Mexico 墨西哥 - 墨 is ink, 哥 is brother, so I though these are dark-skinned people that value brotherhood, masculinity.
South Korea 韩国 - 韩 sounds like 寒, so I just assumed it was a very cold country (isn’t it tho?) Oh BTW, I was in South Korea… in the airport waiting for a transfer flight, never actually entered the country for real, that was 15 years go, the closest I’ve ever been to South Korea. Wanna go there someday, see the snow (cuz its a 寒国 “cold country” remember xD)
Japan 日本 - 日 is the sun, so I thought it gets like very sunny or something
These are the few on the top of my head. You can mention any below and I can tell you what my “subconcious feel” about the name is.
From what I read, a lot of these character choices (with the exception of Japan/Korea, they might have chosen those themselves) were made with the dual considerations of being similar sounding to the country name and the hanzi’s meaning being flattering to the people of the country. And there are plenty of country names that are entirely phonetic (e.g. 意大利 for Italy or 澳大利亚 for Australia, Mexico, etc.).
Japan definitely chose it themselves. Before, the country was known as 倭国, with 倭 meaning something like harmonic but also submissive. Obviously one Tennō wasn’t too happy about that and began signing letters to the Chinese court as “from the ruler of the land where the sun rises (日本) to the ruler of the land where the sun sets.” So Japan became the “Land of the rising sun” (well literally it’s the “sun’s origin”).