Add/fix Woocommerce sorting of products

General information for the website: A website showcasing door handles
Kind of development: Customization of existing website
Description of requirements/features: The website is a Wordpress website running Woocommerce.

The client has asked that he would like to have Alphabetical (A to Z) sorting added to the sorting dropdown in the shop front.

I have attempted to use several plugins that add this type of sorting but none of them have worked successfully.

I need someone to fix this for me.

Along with the A to Z sorting the client would also like to be able to use the 'Custom' sorting feature in the backend as the default sort option in the front end.

Therefore in the sorting dropdown in the shop front there should be:

Custom - (renamed to 'Our Selection')
Sort by Name: A to Z
Sort by popularity
Sort by newness

If you can get all those sort features working together successfully that would be great!
Extra notes: