How do i search authors from search form using author’s name

You should create pre_get_posts filter and trigger in the $query->is_search() to check if post_type is set to author and if it is then unset post_type to posts or what evver you want and set author parametrs to $query object.

related links:

https://codex.wordpress.org/Plugin_API/Action_Reference/pre_get_posts
https://codex.wordpress.org/Class_Reference/WP_Query#Author_Parameters

Or you should create another select, listing all users and give it a name of Author Parametrs found in wp_query

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