Nowadays most people, especially in the West, have Christian names with no obvious meaning. For example, words like "John" and "Marta" are just a set of syllabes that we use to name people, but they have old meanings like "Graced by Yah" and "lady", it's not the same if, nowadays, we named our children with names like "Cloud" or "Star".
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But in the distant past, did people named each other with words of known things? Here a dialogue as an example:
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Oh, hello, Graced by Yah, how are your family?
I am fine, my wife Lotus Flower just gave birth to our third son, we named him Morning Star.
Great! Oh, I have a message from your brother
Which one?
Your older brother, Mountain, he...
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I focused in the cultures from the Europe and Middle East, but you can cite peoples of any part of the world.
By "very ancient" I didn't mean any specific period of time, I just wanna avoid very recent times when many peoples got "corrupted" by the "cultural conquest" of other cultures. I know that many cultures influenced each other since the beggining of the human race, but until when most people had obvious names? Did until the end of the Bronze Age? Until the Roman Empire (before its christianization)?
You might be interested in this older answer I wrote about Ancient Greek names, which did indeed have a direct meaning in everyday Greek language. Even so, most naming conventions were similar to today: people's names reflected their ancestry, social status, religious beliefs and so on.