I actually get custom songs made for my characters! (Mostly because I also make visual novels with them, but also because it's super fun.)
Here's the song for my main character, Battam:
Getting a custom song for your character is actually uh, way more affordable than you'd think it'd be. A simple, looping 1:00 song usually costs anywhere from $40 to $100, depending on who you buy it from-- so I absolutely recommend like, just asking musicians you happen to like on Bandcamp, Soundcloud, etc, if they're open for commissions cuz musicians don't get nearly enough work! Seriously!
And since Tapas let's you put music on updates, you could get a whole OST, have your musician put it up on Soundcloud and viola... a whole soundtrack just for your story! IT'S REALLY FUN, I RECOMMEND IT SO MUCH.