I've seen people saying "No, that girl can't be the Master Sword or the spirit of the Master Sword"...but if you think about it, her being the spirit of the Master Sword makes sense.

The Master Sword chooses its master, and since it's pretty ridiculous for an inanimate object to be sentient enough to "pick its master" or have a mind of its own, having a spirit inside of it would mean that the spirit inside of the sword chooses who its master will be.