The original name is kept only if the original image is used.
If your turn off re-render and don't modify the picture other than changing the size (in other words if you don't rotate, skew or add transparency, contrast etc.), Then the original image and name will be used. Otherwise SiteSpinner creates a new image with a new name
You can change the object name. That name is used to begin the name of a modified image. e.g. if you call your object 'jack', a modified image might be jackgeo1shd2.png
by turning off re-render and sizing the original file won't it be a larger file than if I re-rendered? Would it be a big difference? thanks for all your info.