Here's a trick to appending (or prefixing) your domain to your sitefinity site.

MVC

Global.asax.csView on GitHub
protected void Application_Start(object sender, EventArgs e)
        {
            Bootstrapper.Initialized += Bootstrapper_Initialized;
        }

    void Bootstrapper_Initialized(object sender, Telerik.Sitefinity.Data.ExecutedEventArgs e)
    {
        if (e.CommandName == "Bootstrapped")
        {
            EventHub.Subscribe<IPagePreRenderCompleteEvent>((x) =>
            {
                if (!x.PageSiteNode.IsBackend)
                {
                    var page = x.Page;
                    var siteNode = x.PageSiteNode;
                    page.Header.Title = string.Format("{0} {1}", SystemManager.CurrentContext.CurrentSite.Name, siteNode.Title);
                }
            });
        }
    }</code></pre></div>

Webforms

Edit the code of your masterpage and paste this in

masterpage.aspx.csView on GitHub
protected override void Render(HtmlTextWriter writer)
{
    if (!this.Page.Title.ToLower().Contains( "mysite"))
        this.Page.Title = this.Page.Title + " | mysite.com";
      
base.Render(writer);  

}

It wont work if it goes below the base.Render, so keep it above.

I've experimented and this is the safest place to do it as if you try in prerender, then visit a dynamic generated page with the PageTitleMode set to Append you'd get this

pagename | mysite.com dynamicitemtitle not
pagename dynamicitemtitle | mysite.com