Answer to gleichverteiltes weißes Rauschen is a pleonasm.
It is not a plenuasm. "white" refers to the frequency domain: Since this power spectral density is the same at all frequencies, we call it white as an analogy to the frequency spectrum of white light. (source: wikipedia)
uniform is the amplitude distribution.
These are two independent properties of the signal:
It is often incorrectly assumed that Gaussian noise (i.e. noise with a Gaussian amplitude distribution — see normal distribution) is necessarily white noise. However, neither property implies the other. Gaussianity refers to the way signal values are distributed, while the term 'white' refers to correlations at two distinct times, which are independent of the noise amplitude distribution.
We can therefore find Gaussian white noise, but also Poisson, Cauchy, etc. white noises.