As far as i remmeber, i have seen header(contains logo and site menu) in login page/register page. Sometimes i haven't seen them. On what facts it is done?
You definately do want the company logo/site design on a log in page. When a user enters a site, they know straight away what site their own by the domain, logo, and company name. Often design/branding is also something might recognise. When a user enters a new page for a log in, it's good practice to have the same attributes/properties so that the user knows they are still on the same site, and have not been redirected. I don't think there are pros, in terms of usability, to not have anything. You need to confirm the users confidence that they are logging into the site they think they are, and this is confirmed by the company name, logo, branding and design.
Steve Krug explains this in his usability book, 'Don't make me think', where he explains that that the usability is increased when the user is not thinking or having to work out, in this case, where they are in your site directory.
Take a look at this for more information: https://ithemes.com/dont-make-me-think/