In math, geometry and physics it is common practice to use the coordinates $(u,v)$ to represent an arbitrary parameterization, including those of a surface in a 3d Euclidean space. Since the coordinates of the parameterisation might be arbitrary (it could be 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 coordinates used to index into your texture do not necessarily align with the world space (or view space) coordinates $(x,y,z)$, but is an index into a parameterisation of a surface in that space.