You can use this.GetView(null) to obtain the reference of the view associated to the current VM; then you can obtain the control from the view by name.
As a cleaner solution, you might consider creating a specific RenameNoteViewModel, along with an associated RenameNoteView (containing the textbox and the confirmation button).
Then you can initialize the new view model:
theRenameVM = new RenameNoteViewModel(); //you might also get a factory from the container to build an instance
Once you have a VM set up, you can display it in a popup using IWindowManager.ShowPopup method.
Using this approach you don't have to access the view direclty, leaving your VM easily testable.