Well, you can always use just the name, not the subtitle.
Usually the subtitle (slogan) is just used to bulletin, letterhead etc, but when is for places like churches it can be used just the "Burnips Wesleyan Church", but it all depends of how is the exterior.
Its not a "rule" that you need to use all the entire logo, but is nice to have a "complete" logo (icon and letters) so you can combine sometimes using just the icon, sometimes just the name and sometimes the name, subtitle and icon. It all depends on what are you trying to do. Thats the beauty of design!! :D