What does DNN mean in a TensorFlow Estimator.DNNClassifier?

Give me your definition of "deep" neural network and you get your answer.

But yes, it is simply a MLP and a proper naming would be MLPclassifier indeed. But this does not sounds as cool as the current name.

First of all your definition of DNN is a bit misleading.

There are several architectures of deep neural networks. Inclussive Deep Feedforward Networks is nothing more than a multilayered MLP, plus some techniques to make them attractive.

Some works have used "DNNs" to span all Deep Learning architectures, however, by convention, "DNNs" are used to refer to architectures that use deep forward propagation networks, also called Deep Feedforward Networks

The most important example of a Deep Learning Model is the Profound Net Feedforward or Multilayer Perceptron (MLP). MLP is just a mathematical function that maps some sets of input values to output values. The function is formed by the composition of many simpler functions. You can relate each application of a different mathematical function to provide a new representation of the input.

Therefore, it makes sense that this estimator is called DNNClassifier

My advice is to read this book here.