The admin menu is an administrator module. It uses language constants for its menu items. To see what language constants it uses for each of its menu items, you can check the module's code in the module's template folder /administrator/modules/mod_menu/tmpl/
For example you will see CONSTANTS like :
You can create a language override for the administrator like below:
E.g. for English, create a file named:
Add it in the language overrides folder for the administrator:
Now you can place your overrides as desired in this file, e.g.:
This will override the title for the Global Configuration menu item from "Global Configuration" to "Settings".
Regarding the Components Menu Items:
You need to check in the administrator your language's folder sys.ini language files for the component you would like to create the override. To find its Constant.
E.g. for the Contacts Component (com_contact), check in the en-GB.com_contact.sys.ini, you will see its CONSTANT: COM_CONTACT="Contacts".
You can then use its CONSTANT in your language override file you created earlier and give your desired name.
As an alternative approach, you can use an Extension to create your custom Admin Menu with your custom links. I use a lot the Admin Menu Manager (Free and Paid download) by Pages and Items.
To fully understand how the admin menu works with the Components Menu, you should also study the
getComponents function inside the module's helper file. There you can see that it checks for a few conditions in order to create the final Components SubMenu list.
Part of the code of the helper file (~ line 250):
// Load the core file then
// Load extension-local file.
$lang->load($component->element . '.sys', JPATH_BASE, null, false, true)
|| $lang->load($component->element . '.sys', JPATH_ADMINISTRATOR . '/components/' . $component->element, null, false, true);
$component->text = $lang->hasKey($component->title) ? JText::_($component->title) : $component->alias;
Hope this helps.