Judaism does not prohibit writing the name of G-d, it prohibits only erasing or defacing a name of G-d. However, some avoid writing any name of His casually because of the risk that the written name might later be defaced, obliterated or destroyed accidentally. The commandment not to erase or deface the name of G-d comes from Deuteronomy 12:3. From this, rabbis inferred that we are commanded not to destroy any holy thing, and not to erase or deface His name.
This rabbinic prohibition applies only to what is written in some kind of permanent form, and rabbis decided that writing on a computer is not a permanent form. However, once you print the document out, it becomes a permanent form. That is why many will avoid writing the name out. Generally I will write the name “God” on this website/blog.