'NEVER NEVER NEVER assume that the activeANYTHING will be what you expect!
'Explicitly reference all objects as a practice.
'assuming that xlObj is the Excel Application object
With xlObj.Sheets("Sheet Name Where Chart is")
'assuming that the first chartobject is the correct one...
.ChartObjects(1).Name = MyNewChartName
.ChartObjects(MyNewChartName).Cut
.ActiveSheet.Paste
End With