If a digital picture contains one of the Names of Hashem that may not be erased, may the picture be deleted? What about if it’s in type (eg in word processor)?
It may be deleted.
Most authorities have ruled that there is no prohibition in erasing a Name of Hashem that appears on a computer screen. Various reasons are given for this, the main reason being that writing on a computer screen (certainly a Cathode Tube device, and even an LCD display, neither of which amount to concrete script) is not considered actual script, and that there is therefore no prohibition of erasing.
See Teshuvos Vehanhagos, Vol. 3, no. 326, who suggests a number of further reasons why it is possible that no prohibition applies.