Unless you are going for the Blue in the manga series Pokemon Special/Adventures...
Or was that Green... >.>
It was probably Green.
Ugh... I hate explaining this...
In Japan, the first versions to be released were Red and Green. Thus, the trainer you play was named Red and the rival was named Green. Blue was released later with what was considered to the superior graphics of the Red version. Anyone who has played Green would understand what I'm talking about. When Pocket Monsters was finally released in the United States, they decided to only release the Red and Blue versions because they thought the inferior Green would suffer in sales.
So when Gold and Silver were released, Nintendo of America was faced with a problem. In the game, the rival from Red, Green, Blue and Yellow was called Green, but that version was never released in the US. The solution was simple at the time, just call him Blue instead. It seemed they had already come to the conclusion in the manga as well.
Then FireRed and LeafGreen were released. This time the US did get Green, so now Nintendo was in trouble again. They went with Green for the rival this time because a Blue equivalent wasn't going to be released, which naturally confused everyone who wasn't a
total geek fan. And so, the name Blue fell on the girl this time. Most likely because Blue is more feminine sounding out of the three names.