The Collaborative International Dictionary of English v.0.48:

Surname \Sur"name`\, n. [Pref. sur + name; really a substitution
   for OE. sournoun, from F. surnom. See Sur-, and Noun,
   Name.]
   1. A name or appellation which is added to, or over and
      above, the baptismal or Christian name, and becomes a
      family name.
      [1913 Webster]

   Note: Surnames originally designated occupation, estate,
         place of residence, or some particular thing or event
         that related to the person; thus, Edmund Ironsides;
         Robert Smith, or the smith; William Turner. Surnames
         are often also patronymics; as, John Johnson.
         [1913 Webster]

   2. An appellation added to the original name; an agnomen. "My
      surname, Coriolanus." --Shak.
      [1913 Webster]

   Note: This word has been sometimes written sirname, as if it
         signified sire-name, or the name derived from one's
         father.
         [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Surname \Sur*name"\, v. t. [imp. & p. p. Surnamed; p. pr. &
   vb. n. Surnaming.] [Cf. F. surnommer.]
   To name or call by an appellation added to the original name;
   to give a surname to.
   [1913 Webster]

         Another shall subscribe with his hand unto the Lord,
         and surname himself by the name of Israel. --Isa. xliv.
                                                  5.
   [1913 Webster]

         And Simon he surnamed Peter.             --Mark iii.
                                                  16.
   [1913 Webster]

WordNet (r) 3.0 (2006):

surname
    n 1: the name used to identify the members of a family (as
         distinguished from each member's given name) [syn:
         surname, family name, cognomen, last name]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

SURNAME. A name which is added to the christian name, and which, in modern
times, have become family names.
     2. They are called surnames, because originally they were written over
the name in judicial writings and contracts. They were and are still used
for the purpose of distinguishing persons of the same name. They were taken
from something attached to the persons assuming them, as John Carpenter,
Joseph Black, Samuel Little, &c. See Name.