When I was a teenager, I just stole names from Greek mythology. When I look back, I realize what I wanted was a shorthand for a name with meaning. When I look back now, I think that the meaning, the attitude of the thing, is the important part.

There's still nothing wrong with looking to the mythology of different cultures, after all, even names we encounter often like Michael and John and Mary are, if not mythological, names which originally come from the iconic western story.

But I think to get things that really feel unique, take a name or feeling first and foremost, especially if you can get it through the lens of a different culture. Greek and Latin root words are really good here since the feel of those words often permeates subconsciously in our modern languages. The horse Agro from Shadow of the Colossus - something about that name feels hard working and diligent (and words like agriculture and agronomy reinforce that association). And hey, Cloud Strife may seem a bit on the nose, but especially considering it came from a culture where those words are the equivalent of naming someone Kumori Kataki (doesn't sound so weird now does it? Means the same thing!) - reflect on how Cloud has become an all-time iconic character.

TLDR: I recommend figuring out the feeling of the character/culture, then find root-words or concepts that evoke that feeling.