The nickname Fafhrd comes from around the 7th grade, when one the group of pals with whom I hung around noticed that because of my height, bulk, and affinity for all things Viking, and because of another friend's lack of height, slenderness, agility, and sarcastic wit, we bore a slight resemblence to the Fritz Leiber characters Fafhrd & the Gray Mouser.
My friend and I read the books, and loved the characters. With all the originality of thirteen year olds, we created Dungeons and Dragons characters based on them. Some of our friends began calling us by those names, and they've kind of stuck on me through the years, I suspect primarily because the name "David" is so incredibly common (at one point, anyone name Dave who was introduced into our expanded social circle was called pretty much anything but David, to avoid confusion).
The stories are written about Fafhrd, an exiled barbarian from the frozen northern wastelands, and the Gray Mouser, an orphan raised first by pimps and whores, and then by a gentle hedge-wizard named Glavis Rho. Both of them travel to Lankhmar, the most civilized (and decadent) city-state of Nehwon, and "hilarious hijinks ensue". Well, OK, perhaps not; although there is much humor to be found within, its all dark and cynical.
Fritz Leiber is a throwback to an age when writing was an art form, and the market for fantasy hadn't gotten as pre-packaged and stale as it currenly is. His stories are as long as they need to be; no trilogies expanded to eight or nine books, no padding a one-book plot to make it a trilogy. Everything is self-contained, and expressed with a lyricism and voice unmatched by more modern authors.
These books were originally written as short stories for the fantasy pulp magazines of a bygone age, and collected, with stories written to connect them within a continuity. The original publication order is:
White Wolf Publishing has re-issued these in hardcover, dividing them into four volumes. Information on them is contradictory and hard to find; it looks like the hardcovers collect two books each (more or less), but the paperback editions leave some stuff out. Be safe. Find the Ace paperbacks.
There are a few other editions of some of the stories, mostly from either Donald Grant (who did an excellent set of the novellas with illustrations) and Gregg Press. Gregg Press was a publisher who did library editions of the first six books, and include maps of Nehwon and Lankhmar.
I have an Advanced Reading Copy of a book supposedly published by White Wolf and written by Robin Bailey, the first of a trilogy. I don't think they've actually seen print.
Other things that enthusiasts might look out for include an OLD game published by TSR before their D & D days called Lankhmar, which is notable only for the full-color game map of Nehwon.
TSR also published some Lankhmar material for their AD&D 2nd Edition, adding depth to the city and its inhabitants. While arguably not "canon", the material is entertaining to read.