Depending on your menu setup and how your theme handles menus, this should work as is. If you use the default show pages on menu setting, editors can add pages and they will show up on the menu. They can edit the page title and the new title shows up in the menu.
If you defined a custom menu, an admin needs to initially add the page to a menu, but after that, an editor can alter the page title and it will reflect in the menu.
This is how it works in the default theme, but other themes or plugin may alter this behavior. It may be that the role had a particular capability removed and you may need to reverse that.