Origin image point (image point #0) always exists, and you can't rename it.
If you want to check if another image point with a specific name exists, there is no straightforward way to do this.. If you are sure that the image point "Test" is not set at the same position as the origin, you can do this check:
Sprite.ImagepointX("Test")<>Sprite.x or Sprite.ImagepointY("Test")<>Sprite.y
If the result is true, this means the image point "Test" does exist.
R0J0hound I tested just now and seems like if you try to access ImagepointX or ImagepointY for a non-existing image point, these expressions return coordinates of the origin point, not 0.