I'm way too new to Arm to feel comfortable sharing what I did while naming my character, but over the years, on other games, I've often looked at baby name sites, picked various regions, and then written down the names I liked. Once, I sat down and wrote a list of made-up names, tweaked the letters, rearranged things.
Mostly, when I look at name websites, I pull from a specific linguistic background--Greek, Norse, Hebrew, Arabic, Gaelic, Egyptian, to list a few. It's fun seeing the differences and similarities within each set of names--the structure tends to stay the same within each. Of course, I find languages fascinating, though I only know a smattering of maybe two others besides English.

I wish I knew a lot more.
Fun topic. I personally think names should have meaning, but I've become more accepting of made-up names over the years. I prefer meaning, though, that can be traced, just not blatently taken from well-known books/movies/TV. Those kinda ruin the immersion for me.