Is It Permissible to Delete Hashem's Name from a Computer File?

At the foundation of this question, we need to consider whether it's permissible to turn off a computer or switch to another window when Hashem's name appears on screen, as this seemingly erases the Name. The Rambam wrote (in Chapter 6 of the Laws of Foundations of the Torah):
Whoever erases one of the holy Names transgresses a negative commandment, as it is stated regarding idolatry, "You shall destroy their name from that place; you shall not do so to Hashem your God." This is also ruled in the Tur and Shulchan Aruch Yoreh Deah (Section 276:9).

Similarly, we should consider whether erasing Hashem's name recorded on a tape recorder is prohibited due to the prohibition against erasing the Name.

Our great teacher Rabbi Ovadia Yosef of blessed memory, in his responsa Yechaveh Daat Part Four (Section 50), discussed this issue. After citing the Rambam, he wrote that it seems more likely that since there are no actual letter forms on the tape at all, but rather sound waves captured electronically in a form that cannot be seen by the human eye, therefore there is no basis to prohibit erasing them through another recording, even though the holy Names can be clearly heard through electrical means.

He brought several proofs for his position, including from what we learned in the Talmud in Tractate Gittin (19b), that a divorce document written with "mei milin" (a type of ink that disappears after some time, and if one wants to see it again, one passes over it water from pomegranate peel, and then the writing becomes clearly visible again, as Tosafot explain in the name of Rabbeinu Chananel) is not valid at all, even though afterward the writing can be seen using pomegranate peel water. Nevertheless, when it cannot be seen with the eyes, it is not considered "writing" sufficient to validate a divorce document. From here we learn that it is also not considered "writing" worthy of being considered a "holy Name" that is forbidden to erase.

From here, regarding Hashem's name written on a recording tape, even though it can later be heard through electrical action, it is not considered "writing" that would be forbidden to erase. From this, we can also learn regarding Hashem's name stored in a file on a disk, that it is permissible to erase it without concern, since it is not visible to the eyes at all.

However, this is not sufficient to permit erasing Hashem's name that currently appears on a computer screen. Seemingly, we should say that all that Rabbi Ovadia of blessed memory permitted regarding erasing Hashem's name applies specifically when the Name is not visible to the eyes, but if it is currently visible to the eyes, we should be stringent about this.

However, we have an additional reason to be lenient in this matter, based on what Rabbi Ovadia added, that there is a dispute among poskim whether it is permissible to erase Hashem's name that was not written with sacred intent (when writing Hashem's name in a Torah scroll, the scribe declares that the Name is written for the sanctity of the Name, but an ordinary person writing Hashem's name does not intend to sanctify the Name), and many poskim hold that it is technically permissible to erase a name that was not written with sacred intent.

Particularly regarding a name written on a computer, where there is no actual writing, but rather aggregated lights and similar things that cannot have holiness applied to them since they are not tangible things, it seems certainly reasonable to say that holiness does not apply to these names according to all opinions.

In truth, there are arguments to be made on both sides, but the essence of the matter is that any writing that is not actual writing cannot have the holiness of the Name applied to it, and therefore the practice of erasing Hashem's name by turning off the computer, or switching to another window or similar actions, involves no prohibition at all. We also asked Rabbi Ovadia Yosef of blessed memory about this, and he responded that in practice there is no need to be concerned about prohibition, and it is permitted both to delete computer files containing holy Names and to turn off the computer when Hashem's name appears on the screen.

In summary: There is no prohibition against erasing holy Names in computer writing, only in actual physical writing.