Calling function in usercontrol from page

Instead of trying to find or keep track of controls (which may change in future versions of your code) and modifying them with code at runtime, I would go with a more data-centric method - WPF/Silverlight are made for this.

Generate a business application sample from the visual studio project templates...check out the LoginStatus.xaml/LoginStatus.xaml.cs files to see another way of doing this with bindings and visual states.
Basically, there's a singleton/static object that represents the logged-in/logged-out state. This class has events for loggedin and loggedout. Any element (like a usercontrol) you have that needs to know when the state changes can subscribe to these events and in the event handlers set its state appropriately (like changing a "log in" button to "log out"). This puts the code right in the usercontrol's class instead of having to track or find usercontrols from other pages/controls.

For example, if you wrapped your authentication code in a singleton class like this

public class AuthenticationService : INotifyPropertyChanged
{
    #region INotifyPropertyChanged Implementation

    public event PropertyChangedEventHandler PropertyChanged;
    void OnPropertyChanged(string name)
    {
        if (PropertyChanged != null)
        {
            PropertyChanged(this, new PropertyChangedEventArgs(name));
        }
    }

    #endregion

    private static volatile AuthenticationService instance;
    private static object syncRoot = new Object();

    private AuthenticationService()
    {
    }

    public static AuthenticationService Current
    {
        get
        {
            if (instance == null)
            {
                lock (syncRoot)
                {
                    if (instance == null)
                        instance = new AuthenticationService();
                }
            }

            return instance;
        }
    }

    public event EventHandler<EventArgs> LoggedIn;
    public event EventHandler<EventArgs> LoggedOut;

    public void LogIn()
    {
        //if and when loginsuccessful
        //{

        IsLoggedIn = true;

        EventHandler<EventArgs> evnt = LoggedIn;
            if (evnt != null)
            {
                evnt(this, new EventArgs());
            }
        //}
    }

    public void LogOut()
    {
        //if and when logoutsuccessful
        //{

        IsLoggedIn = false;

        EventHandler<EventArgs> evnt = LoggedOut;
        if (evnt != null)
        {
            evnt(this, new EventArgs());
        }
        //}
    }

    bool _isLoggedIn = false;
    public bool IsLoggedIn
    {
        get { return _isLoggedIn; }
        set
        {
            if (_isLoggedIn != value)
            {
                _isLoggedIn = value;
                OnPropertyChanged("IsLoggedIn");
            }
        }
    }
}

...then a usercontrol that needs to update itself based on the loggedin/loggedout status can simply do something like this

public MyUserControl()
{
    InitializeComponent();

    // Subscribe to loggedin/loggedout events so we can update our UI
    AuthenticationService authentication = AuthenticationService.Current;
    authentication.LoggedIn += new EventHandler<EventArgs>(authentication_LoggedIn);
    authentication.LoggedOut += new EventHandler<EventArgs>(authentication_LoggedOut);
}

void authentication_LoggedIn(object sender, EventArgs e)
{
    // Change button text to "Log Out"
}

void authentication_LoggedOut(object sender, EventArgs e)
{
    // Change button text to "Log In"
}

No need for another page to know about MyUserControl :)