Personally, I wouldnt move it to a folder called Wordpress. The trick with Wordpress is to try to prevent bots/visitors from knowing that you are using Wordpress. The reason is if they know you are using Wordpress then there is a series of things they can try (the might not succeed) to get into your wp-admin.
With that in mind, I would move it to a folder with your website name in it.
Now how to get your website working in that subfolder.
Do you have access to PHP MY ADMIN? Who is your webhost?