WordPress Logout page is remain in the Login page when you logout from your WordPress account. It doesn’t have any built-in option to change it. but I have solve this problem with adding some basic code to the function.php file of the current applied WordPress Theme. It work perfect but doesn’t have function and not more flexible. Instead you can use some WordPress plugin.
WordPress Redirect Logout page Using Code
if you want to go directly to the front page when you log out, place this code into your functions.php in your current theme.
wp_redirect( home_url() );
The code must be placed at the end of all code. See the screenshot.
WordPress Redirect Logout page Using WordPress Plugin
With plugin you can choose which URL users are directed to when logging out of WordPress. You redirect the users to some page such a network homepage, Help and Support, Sales page, Special offer for existing users and even to the specific product of the company.
So for more function and options, the best case is using plugin. The best plugin I recommend you is Logout Redirect plugin.
It is easy, simply install the plugin and follow the How to redirect WordPress Logout page to any page you want.
Read WordPress document for Function Reference/wp logout url help.
Hop it would be helpful and can solve your WordPress problems.