WPF equivalent of the AccesibleName property
AutomationProperties.Name
is the attached property you are looking for.
You can either specify it directly in XAML:
<object AutomationProperties.Name="name" .../>
Or using the getter/setters on AutomationProperties:
using System.Windows.Automation;...AutomationProperties.SetName(control, "name");
...or...
control.SetValue(AutomationProperties.NameProperty, "name");