Hello,

I’m using claims authentication as shown here

 public bool UserLoggedIn(UserProfile userProfile)
        {
            var userCredentials = new[] {
                    new Claim("UserId", Convert.ToString(userProfile.UserId)),
                    new Claim("Username", Convert.ToString(userProfile.Username)),
                    new Claim("Firstname", Convert.ToString(userProfile.Firstname))};

            var id = new ClaimsIdentity(userCredentials, "Forms");
            var cp = new ClaimsPrincipal(id);
            var token = new SessionSecurityToken(cp);

            var sam = FederatedAuthentication.SessionAuthenticationModule;
            sam.WriteSessionTokenToCookie(token);

            return true;
        }

In my site the user has the option to change his name, how can I update the Firstname value inside the above the claims authentication?

Reissue the cookie with the new claims, just like the login page does above.