I found an example (of Akizuki) here http://arxiv.org/pdf/alg-geom/9503017v1.pdf

Thank you for the hints and yes Youngsu, that is what I wanted to ask. Also it is known that under the assumptions above, $D$ is analytically irreducible if and only if $D$ is unibranched and $D'$ is finitely generated as $D$-module if and only if $D$ is unibranched and the $\mathfrak{m}'$-adic topologyon $D'$ induces the $\mathfrak{m}$-adic topology (where $\mathfrak{m}'$ is the maximal ideal of $D'$)