Well...let's see...
To be perfectly honest, I originally went with the name of CBoy (don't ask. I was a young kid/young teen going through a superhero fan phase for a few years. I grew out of this, and you'll learn why in a bit), then later Avalon (which I still use at times, but not for the same character idea) and Aragorn, the latter two especially when I was playing Artix Entertainment's browser games (been a fan of the company and staff ever since I first played DragonFable). To say the least, I had a couple staple names that weren't really that original.
However, a couple years before college (long after I grew out of the "phase" I pointed out earlier), I started gaining an interest towards other cultures and history. Mostly because I knew enough about my own culture that it started getting boring to pursue knowledge about it (I'm sure we've all had that happen at one point or another). This led me to learning about star signs, Greek mythology, and other Greek-related information, and one name that came up was Chronos, the personification of Time. Didn't really pull too many ideas from that (though I did have a few thoughts for a character that could manipulate time to an extent and always reincarnated), but the name definitely stuck around in my head for a while, and as you can tell, I eventually used it (to the point of even changing "CBoy" to "Chronos" in DragonFable first chance I was able to change my character's name).
At a later point, my interest in places outside of America turned towards Eastern culture (namely Japanese culture), partially due to having played games or parts of games with obvious draws from it (most notably: Sheena + Mizuho and its residents in Tales of Symphonia, and all of Okami). It was sometime during my early interest that I saw a classmate playing an MMO during break between courses: Dynasty Warriors Online (which also happened to be the first Warriors game I ever played, and what drew me towards the Warriors games). It caught my interest right away, and I downloaded and installed it first chance I had. Since it was the first non-browser MMO that I played, and I wasn't sure if I would play any others, I wanted a name that would stick. Chronos was obvious since I was using it more, but I had trouble thinking of a last name. But then I thought about some of the Japanese names I had heard, and while I didn't know much about the Japanese language at the time, I decided to make a name that sounded close enough to work.
Hence, I created the surname "Notashi" for my character, and, with the exception of two instances ("BowieSage" in Dragon Nest and "ClessAlbeon" (screwed up on the last name, but I definitely thought of Cless/Cress from "Tales of Phantasia") for another game), the name "Chronos Notashi" became a regular name for my character, especially for more Eastern/Japanese-themed settings. Though usually for more non-anime-style European/American/sci-fi-themed game, my in-game name (my forum name is usually Chronos Notashi, again with exceptions such as Dragon Nest) is typically just "Chronos" (or in the case of PSO:BB due to wanting Skyly and not knowing about the name change until AFTER level 20, Chro-nos), or I might even go with a more "American" last name. I also sometimes use longer hairstyles for medieval versions of my character (my HUmar uses one such hairstyle as well) for a bit more of an adventurer/knight-style appearance.
By the way, if it's okay (though this is Off-Topic, so I assume no one will mind), I'll share a screenshot of my DWO character (the first time I used "Chronos Notashi") in case I change my profile image at any point.