Solution 1.:
(Modified after the comment of @CarLaTeX)
\documentclass{article}
\usepackage{venndiagram}
\begin{document}
\begin{venndiagram2sets}[shade=blue,tikzoptions={opacity=0.5},labelA={},labelB={}]
\fillOnlyA
\setpostvennhook
{
\draw (labelA) node[above=2pt] {A};
\draw (labelB) node[above=2pt] {B};
}
\end{venndiagram2sets}
\end{document}

Solution 2.:
You could use tikzlibrary
calc
, and with its help, it's easy to put the labels on certain coordinates.
(I used @Jake's answer for TikZ: Node at same x-coordinate as another node, but specified y-coordinate?)
\documentclass{article}
\usepackage{tikz}
\usepackage{venndiagram}
\usetikzlibrary{calc}
\begin{document}
\begin{venndiagram2sets}[shade=blue,tikzoptions={opacity=0.5},labelA={},labelB={}]
\fillOnlyA
\setpostvennhook
{
\path let \p1 = (labelA) in node at (\x1,3.2) {A};
\path let \p2 = (labelB) in node at (\x2,0.2) {B};
}
\end{venndiagram2sets}
\end{document}
