No, you cannot create an alias for term names.
But if you could, it would not be the optimal or easiest method.
Instead of having a single taxonomy were the top level is the OS, the children are the price, and the grandchildren are the app category, instead have 3 taxonomies:
- Operating System ( iOS/Android/etc )
- Pricing ( free/freemium/paid/etc )
- App Type ( Health/Medical/etc )
Make App type a hierarchical taxonomy so that you can nest sub types category style.
This way you side step your problem entirely, and can list all free apps, or all Apple apps, or all medical apps. Your problem is now one of implementing taxonomy intersections, which is a solvable task, and one you don’t even have to solve.
For example, lets say your post type is application, with an archive at example.com/apps and you have an operating_system and pricing taxonomies, you could go to this URL to view all free apps for iOS:
example.com/apps/?operating_system=ios&pricing=free
This should make implementing the search functionality you’re building incredibly simple as you can make operating_system or pricing input fields in the search form and use the GET method
You could apply rewrite rules to create URLs such as:
example.com/apps/ios/free
But I won’t cover rewrite rules as that’s a separate topic you should ask about.
I would note that you can write code that makes use of wp_insert_term or wp_set_object_terms to assign and create terms in the 3 new taxonomies for each post, based on the existing taxonomy you’re using.
In the end, your data structure is broken, and what you want cannot be done without restructuring ( which is not impossible )