Maybe change background color of each MATLAB instance so you can differ them.
Short expansion on comments above,
desktop = com.mathworks.mde.desk.MLDesktop.getInstance;
If you open the editor in undocked mode, evaluate the line with F9
jEditor = desktop.getSelectedClient;
jEditorGroup = jEditor.getGroup;
By using uiinspect on jEditor and jEditorGroup it's possible to see these these values you're looking to change.It's not possible to change them, as it looks like those values are determined on the new file creation or loading.