you can use cookies to store information and once user click on Logout button then simply clear the cookies
// A Visualforce controller class that creates a cookie
// used to keep track of how often a user displays a page
public class CookieController {
public CookieController() {
Cookie counter = ApexPages.currentPage().getCookies().get('counter');
// If this is the first time the user is accessing the page,
// create a new cookie with name 'counter', an initial value of '1',
// path 'null', maxAge '-1', and isSecure 'false'.
if (counter == null) {
counter = new Cookie('counter','1',null,-1,false);
} else {
// If this isn't the first time the user is accessing the page
// create a new cookie, incrementing the value of the original count by 1
Integer count = Integer.valueOf(counter.getValue());
counter = new Cookie('counter', String.valueOf(count+1),null,-1,false);
}
// Set the new cookie for the page
ApexPages.currentPage().setCookies(new Cookie[]{counter});
}
// This method is used by the Visualforce action {!count} to display the current
// value of the number of times a user had displayed a page.
// This value is stored in the cookie.
public String getCount() {
Cookie counter = ApexPages.currentPage().getCookies().get('counter');
if(counter == null) {
return '0';
}
return counter.getValue();
}
}
You can also use Javascript cookies but keep in mind that
The setCookies method adds the prefix “apex__” to the cookie names. so in javascript cookies append apex__ .
javascript Cookies Example
function setCookie(cname, cvalue, exdays) {
var d = new Date();
d.setTime(d.getTime() + (exdays*24*60*60*1000));
var expires = "expires="+d.toUTCString();
document.cookie = cname + "=" + cvalue + "; " + expires;
}