I always sign my artwork. I may not be the best artist, but due to seeing a lot of other artists get their work stolen, I'm a bit paranoid about it. I usually sign my name at the bottom of the drawing ion the far right corner(if drawn on paper first), or if I forget to, I type it in the same spot, then lower the opacity to make it harder to erase without it being obvious. Occasionally, I'll place it in the middle of a drawing, if it's a very small drawing, or, if the situation calls for it, I'll place it in the left corner of a drawing.
As for the name I sign, it depends on what I'm drawing, or where the drawing's for. If it's for Gaia, I always use my Gaia name. If it's for my Deviantart site, I always use my standard pen name, unless it's a Maple Story fanart, in which I sign my MS pen name, Mino(named off of one of the characters in that game.)
I try to stick to my standard pen name, but half the time, I can't, due to naming myself something different there.(I have a hard time sticking to one user name.)