The right way to do this is:
(1) Make sure you have either the primary key, or at least a unique index, defined on ( last_name, first_name)
(2) Go ahead and just try to make the insertion.
(3) If it fails, and if the reason is because of a unique-key violation (the method for determining this is, alas, database-dependent, but in general it involves inspecting the resulting error message) then you can tell the user they have to choose another name.
This is this the only guaranteed safe way to do this with SQL: if you lookup the name first, you have no guarantee that some other user isn't trying to add the same name at the same time. What's more, since in the large majority of cases someone else already doesn't have the same name (assuming you're not AOL or Earthlink, that is!) it's actually less overhead then doing a SELECT before every single INSERT.