Linden Lab Official:Can I have a custom last name for my Second Life account?

Second Life® account names are created by inventing a first name, and selecting a last name from a list. These names cycle in and out of usages as residents choose them. This creates a good variety of in-world names, gives residents some identity through the rarity of their last name, and most importantly, allows residents to use common first names (there's always a good chance you can be "Dave" Someone), thus avoiding the awkward names on some other services (like "dave298374") that can remove some of the individuality of the world.

Under special circumstances, you can create your own last name- See Custom and Vanity Last Names for details!