Thanks for contacting Syncfusion support.
Since DockingManager is not an ItemsControl we can't change HeaderTemplate dynamically using Binding. But our TabControlExt will support this and please have the sample for the same from below location.
Sample link : TabControlExt_F118928.zip
Edit the textbox in content area of TabControlExt and observe the changing of Header of TabItemExt.
Please let us know in case of any other queries.