I personally like this name. It's very pretty. Of course, I say it as "bell-on-a" but, I like it. I thought that maybe a girl with the name could be nicknamed "Belle" — which was thought to be the French word for "beautiful." And the "to fight" meaning is very nice for modern girls. I could personally picture myself naming a daughter this.
The original form of Bellona is Duellona, after 'duellum', the ancient and initial Latin word for "war". Later, when over time 'duellum' changed into 'bellum', the name of the goddess was altered accordingly as well.
Superiority in war was the primary thing that made the Romans great, before even their cultural or architectural achievements. They conquered half the world for a reason. It's hard to imagine that any real person would actually live up to the implications of this name, and it's hard to imagine anyone who would want their daughter growing up to do so. Probably best for fictional people.
Name of the city in "Dhalgren" by Samuel R. Delany. Something happened in Bellona which is never explained, but the city is always on the edge of total destruction. Almost no appliances work, it's mostly abandoned, buildings suddenly burst into flame then are fine the next day. It's completely separate from reality.
I don't think the meaning's awful. You don't have to interpret "to fight" as something negative. One can fight for a dream, for his/her life, for chances. I think it's a strong meaning.