In math, geometry and physics it is common practice to use the coordinates $(u,v)$ to represent an arbitrary parameterizations, including those of a surface in a 3d Euclidean space. Since the coordinates of the parameterisation might be arbitrary (it could an angle, or a function of the Euclidean coordinates $(x,y,z)$, or something else), it is helpful to distinguish them from the coordinates used to represent the wider Euclidean space in which the surface exists.
The $(u,v)$-notation caught on in computer graphics for the same reason: it clarifies that the surface that your texture is mapped onto is not necessarily aligned with the world space (or view) coordinates, but is a parameterisation of that space.