Kind of. To be exact, it can be written in documents that are to be preserved and taken care of -- e.g., a Torah. But the Name should not be written out in casual correspondence not because it is bad to write the name, but because the casual correspondence can (and probably will) be disregarded and disposed of improperly and in a disrespectful manner.
The source of the prohibition comes from #3 on the list "using the L-rd's name in vain" and a specific command to erase the names of various fake "gods" of the Cannanites (I think, one of the crapfest tribes that used to surround us, anyway) -- the opposite of which is preserving the Name of G-d.
Given that the Internet is profoundly temporal, it's particularly appropriate.