Just send the node.label as a parameter to your function:
#{treeController.onSaveNodeLabel(node.label)}
So, in your web page:
<p:inplace editor="true" event="dblclick">
<p:ajax event="save" listener="#{treeController.onSaveNodeLabel(node.label)}" update="@this" />
<p:inputText value="#{node.label}" />
</p:inplace>
And in your bean:
public void onSaveNodeLabel(String nodeLabel) {
//
}