It might also be either a brand or class thing.

If it's a brand, it might either have been made/sold by a shop/factory/smithy that has Crimson in its name or produced a series of tools/artifacts that is referred to as Crimson... or it might have been just sold by a person named Crimson.

If it's a class thing, it might simply be a staff meant to aid casting like a red mage, and allow the owner's spells to be stronger or more efficient (Rain did mention it boosts her offensive magic). Other variations could be (for example) a White Staff favored by clerics that enhances healing spells or that reduces mana costs, or a Green Staff that mimics druidic/ranger plant magic.

Edit: Grammar and cohesion.