En nombre puede obtener de la clase ServletContext.Con JSF
ExternalContext externalContext = FacesContext.getCurrentInstance().getExternalContext();
ServletContext servletContext= (ServletContext) externalContext.getContext();
System.out.println("Context Name: "+servletContext.getServletContextName());
Или внутри сервлета
protected void doGet(HttpServletRequest request, HttpServletResponse response)
{
ServletContext servletContext= getServletContext();
System.out.println("Context Name: "+servletContext.getServletContextName());
}