Well if it would need to persist, you would have to create a UD field in a UD table or something. But as for setting the tab text, use:
//Add these to your using statements
using Ice.UI.App.(name of your dashboard goes here);
using System.Linq;
public void InitializeCustomCode()
{
// ** Wizard Insert Location - Do not delete 'Begin/End Wizard Added Variable Initialization' lines **
// Begin Wizard Added Variable Initialization
// End Wizard Added Variable Initialization
// Begin Wizard Added Custom Method Calls
// End Wizard Added Custom Method Calls
MainDockPanel mainPanel = (MainDockPanel)csm.GetNativeControlReference("D1E2D613-8F6D-4014-AD5C-F68870E1EC69");
var firstTab = mainPanel.baseDockManager.ControlPanes.Cast<Infragistics.Win.UltraWinDock.DockableControlPane>().Where(x => x.TextTab == "test").FirstOrDefault();
firstTab.TextTab = DateTime.Today.ToString();
}
This helped me figure this out