Is noise a random process?
Adding to @Kaz's answer, noise is normally modeled as a random process. Even an interfering RF carrier or hum can be modeled as a random process (random phase sinusoid).

The theory of random processes is very elegant and allows for simple analysis of systems with "noise".

Moreover, even deterministic components such as quantization or rounding errors are modeled as random processes (independent of the actual signal) in order to study system performance. And these approximations are quite good in general.