As a sometimes teacher of the fine art of painting, one of the more interesting observations on my part is the perplexing problem amongst novice painters as to how to sign their work. Like our handwriting, signatures on paintings go right to the heart of the artist's personality. I've seen high school students (usually boys) without a great deal of discernible talent, I might add, sign a modest, 12"x16" canvas with their full name, stylishly spelled out with great flourish in letters an inch tall (I kid you not). And I've had little old ladies in adult classes who had to have their arms twisted in order to even add their initials a quarter inch tall down in the corner where it would, in all likelihood, be totally covered up with the frame, so the situation runs the gamut. In any case, apparently it is often one of the more difficult parts of the painting for most beginning artists. It would seem that "coloring" in paint is one thing, actually being able to write (or print) legibly with clumsy old brushes and cantankerous, thick, oil paint, is something else altogether.
The only thing I might add to this discussion is advice I was given by a wise, old, Indian guru atop one of the highest peaks in Stockport, Ohio. It was something to the effect that one's fully legible, complete signature (first and last name along with date) is probably the BEST form of advertising you could possibly have as an artist; and the great part is it's FREE! Now, having said that, I've NEVER used anything more than "J.Lane, (year)" with any of my paintings or drawings, so take this with a grain of salt, from one who's never followed such sage advice. Whatever the case, if an artist is clever and can master the technical virtuosity to keep his or her signature reasonably small, it can become a PART of the painting to such a degree that, while still readable, it in no way detracts from the painting. Just don't get it down so low it'll be covered up by the picture frame.
As far as other artists are concerned, the inimitable Mr. Van Gogh never used anything more than "Vincent." On the other hand, our good friend Mr. Rockwell at various times in his career used simply "N.R.," then moved on to "norman rockwell" (in script), and finally the large, hollow, Roman letters we've come to know and love, spelling out for all the world to see, "Norman Rockwell." Monet used simply "Claude Monet" (occasionally just "Monet"). Albrecht Durer used a stylized "AD" logo. Michelangelo only signed one work in his entire life, and it was a SCULPTURE, not a painting (the Vatican Pieta). Abstractionists almost NEVER sign their work (on the front at least) though Willem de Kooning is an exception to that rule (last name only). Stuart Davis signed his graphics-laden work with his full name large enough to read from twenty paces on a moonless night. Picasso was totally indifferent about his signature, only occasionally signing his work. Jan van Eyck, on the other hand, signed one of his best loved paintings, the "Arnolfini Wedding" with great, elegant calligraphy, right smack dab in the MIDDLE! So, who's to say what's right? Well, okay, art historians and authenticators would prefer you use something nice, modest, and above all, decipherable, somewhere down in a lower corner--so there.