First thoughts are things unoriginal like "Ember" or "Cinder", which also have a basis in fire, which you said she actually doesn't control. From there my mind goes to musical terms like clef notes and such, none of which are giving birth to good names.
In my experience when drumming up names, if you want a theme with them, say in her case for music, try looking for Hebrew musical words, terms, and names. Maybe something there will pop.
Of course when all else fails, I just babble. I start with more or less what I think the name might sound like (Like Fantla for example), then just spout random nothings. Every now and then, one of those nothings becomes a glorious something.
Hmmmm.... Fantla..... *Writes that one down for future consideration.* (Though feel free to use it. It'd be tertiary character at best in anything I do. More likely I never will unless it evolves into something else.)