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][1] 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 space) coordinates, but is a parameterisation of a surface in that space.


  [1]: https://en.wikipedia.org/wiki/Surface_(mathematics)