If you replace the WordPress logo image (wordpress-logo.svg) in the /wordpress/wp-admin/images folder, you can display any image or logo you want in the Password Protected page. You will need to adjust the background-size setting as well as the margin, height & width settings.
Next open the password-protected-login.php file located in /wordpress/wp-content/plugins/password-protected/theme and add your adjustments to the section
<style type="text/css" media="screen">
#login_error, .login .message, #loginform { margin-bottom: 20px; }
.login h1 a { background-size: 700px auto!important; height: 100px!important; width: 700px!important; margin: 0px -200px 25px;!important;}
</style>
Other adjustments include:
.login h1 a {
background-image: none, url("../images/wordpress-logo.svg?ver=20131107");
background-size: 700px auto;
background-position: center top;
background-repeat: no-repeat;
height: 100px;
font-size: 20px;
line-height: 1.3em;
margin: 0px -200px 25px;
padding: 0px;
width: 700px;
text-indent: -9999px;
outline: 0px none;
display: block;
}