Is it permissible for the name of Allah to be in my signature, or not?

Signing with "Allah" (God) on websites and forums is a good deed and a reminder of Allah. As for signing with it on papers, its ruling depends on the fate of those papers: If the signer knows that they will be disrespected, then it is impermissible. If he knows that they will be preserved and not disrespected, then there is no harm. The names of Allah and whatever the Shari'ah has glorified must be protected from disrespect, either by placing them in a suitable location, or by disposing of them through burial in pure places, or burning, or shredding with a shredding machine.