Actually one of several "fathers." Caution: the following is for the DSP engineers among you. :-)
When I learned communications theory it was attributed to Claude Shannon (his 1948 paper) and sampling theory to Nyquist. I do remember my father once telling me that E. T. Whittaker had published the relevant mathematics long before Shannon, but I never looked up the history. And I never asked my father to elaborate as he was pushing his copy of Whittaker and Watson at the time, together with the idea I should be a mathematician or a physicist – not an engineer!
But on the plane back from Paris I read the June issue of Communications Engineer from The Institution of Engineering and Technology which included an interesting article on V. A. Kotelnikov by Professor Chris Bissell.
... in the late 1940s <Shannon> wrote that the sampling theorem was “common knowledge in the communication art, but in spite of its evident importance it seems not to have appeared explicitly in the literature of communication theory.” But Shannon was only partly correct. Ideas about sampling were indeed common knowledge in the late 1940s, and the theorem in various forms had appeared in the mathematical literature. But the theorem had also been published in the ‘literature of communication theory’ as early as 1933. Trouble was, it was published in the proceedings of a conference in Stalinist Russia – and in Russian.
The article goes on to give Kotelnikov credit for putting the problem of sampling a continuous, band-limited signal into an engineering context. Now that I'm back home and on-line again, I've been able to track down more of the story and access an English translation of Kotelnikov's seminal 1933 paper, On the capacity of the 'ether' and cables in electrical communication. Not surprisingly, Wikipedia has an even more complete historical background on sampling theory in communications.
Suffice it to say, "Whittaker-Kotelnikov-Raabe-Shannon-Someya sampling theorem" would be a better name, as many people reached similar conclusions with varying degrees of parallelism. Kotelnikov suffered from writing in Russian under Stalin and before the west started tracking Russian science.
Even with the English translation of Kotelnikov now available, Shannon's 1948 paper remains the best and most complete source for me. I think it's only available in hardcopy forms, but other URLs of possible interest are here.