The easiest way to do this without editing the page.php template in your theme is to add it as a custom field, then use a plugin (or code) to display that custom field in the control panel on your Pages list. The plugin I’d recommend is Admin Columns. It’s free and highly-rated. Once that’s installed, go through these steps:
First, edit any Page. Find the Custom Fields panel. If you can’t find it, it might be hidden by default. To un-hide it, if you are using the Classic editor, go to the top-right where it says “Screen Options” and make sure the “Custom Fields” box is checked. If you are using the new Gutenberg / Block editor, go to the 3-dot menu at top right, scroll to the bottom and select Options, then check the box for Custom Fields. Click ‘Enable and Reload’. Now the Custom Fields panel should appear below the page’s content. (You’ll only have to do that once.)
In the Custom Fields area that appears below the Page content, add a field with the Name admin_title (no spaces). In the Value area, put the name you’d like displayed in the control panel only. Save the Page.
Now go to Settings > Admin Columns and choose “Pages” from the dropdown if it’s not already selected. All the current columns displayed on the Pages list page will appear here. You can delete the ones you don’t need, drag-and-drop to rearrange. Click Add Column, then in the Type dropdown, choose “Custom Field”. Change the Label to Admin Title (or whatever). In the Field dropdown, select your admin_title field. In the Field Type dropdown, choose Text. Set Inline Editing to Yes. Save.
Now back over to the Pages screen. You’ll see your new field in one of the columns. Above the list of all Pages, there’s a new small “Inline Edit” option. Turn that on, and little pencils will appear as options in the Admin Titles areas – this allows you to edit these custom fields directly from this page (if you want) instead of having to open each Page to add titles.