Not all shapes have a name property (like a geoline for example). Here is a basic sample that might help. Create a shape (Rectangle,Oval or Circle) and name it "MyShape"
Code:
Dim objshape As MapPoint.Shape
For Each objshape In MappointControl1.ActiveMap.Shapes
Select Case objshape.Type
Case 1 ' An AutoShapeType (Rectangle,Oval or Circle)
If objshape.Name = "MyShape" Then
MsgBox "Do Something"
End If
End Select
Next