May one delete something on a computer that has the G-d’s name written on it?
The image on a computer screen is not an actual "Shem" (the name of G-d, which may not be erased). It may be likened to a papercut which casts the shadow of a "Shem". We consider this "Shem" an image, not a real object. Nevertheless, some people refrain from directly erasing a "Shem" on the screen, as it looks like erasing, but would replace it with another word, or delete the file when it is off the screen. Similarly, Rav Ovadiah Yoseh says it is not forbidden to erase a tape which has a name of Hashem in it but it is preferable to tape over it than simply erase. When a "Shem" is in a document the document may be deleted, as well as a section of the document, though it is preferable to do this when the "Shem" is not on the screen. Again, this is a stringency because it looks like erasing, but it is not really a "Shem".