Can I make the search by name filter work on my multilingual website? (search by arabic names and by english names when switching

So I have a post grid of members on my website translated via transaltePress to arabic. I am trying to make the search filter works on both languages. For now, it is just working on the english version of all the titles / names. Also, ordering the items in alphabetical order is done just on the english version but the arabic version is following the order of the english one. Can i differentiate between them?

Best regards,

Ali