Trying to come up with a name completely from scratch is hard, and probably won't seem very 'natural' regardless. Mankind has a few thousand year's worth of names, and there's nothing stopping you from modding them.
My go-to website has always been
babynames.com, funnily enough. I come up with something related to the character, use that form to search by meaning, and ponder everything that comes up. If nothing immediately strikes me as 'Yeah, that sounds good', I'll either:
1) Try searching for another trait or whatever related to the character.
2) Start disassembling the names into component syllables and messing with the sounds/feel of the name. (I can do this in my head but a friend swears by saying them out loud).
3) Usually, I'll have the first letter of the name in mind, or will have decided on one by this point. If I see something that's not quite right, I'll figure out what origin the name has and then look up by origin and just browse 'til something feels right.
Basically, I look around for inspiration and then tinker with what I find.