This doesn't double click but returns a name when selected:
Sub GetBlkName()
Dim acObj As AcadObject
Dim vbasePnt As Variant
ThisDrawing.Utility.GetEntity acObj, vbasePnt, "Select Block"
If acObj.ObjectName = "AcDbBlockReference" Then
MsgBox "This block is named " & acObj.Name
Else
MsgBox "This is not a block reference"
End If
End Sub