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

When you sign up for Second Life®, you create your account name by entering a first name, and selecting a last name from a list. The last names cycle in and out of usage as Residents choose them. This creates a good variety of inworld 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 reduce individuality.

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