I am currently studying vectors and matrices in 3 dimensions, my book calls the unit vectors i j and k, however I have seen them being called in other ways, such as: x-hat, y-hat and z-hat; or simply any letter with a ^ on top. Which is the more correct way to call the unit vectors?
There is no "more correct way". It all depends on convention. Some people prefer $\vec i, \vec j, \vec k$, some people prefer $\hat x, \hat y, \hat z$, some people prefer $e_1, e_2, e_3$... No choice is truly objectively better than the others. My preference tends towards $e_1, e_2, e_3$ becauses it easily generalizes in higher dimension, for example, but in small dimension letters are just fine.