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The Collaborative International Dictionary
Surnaming

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.

Another shall subscribe with his hand unto the Lord, and surname himself by the name of Israel.
--Is

  1. xliv. 5.

    And Simon he surnamed Peter.
    --Mark iii. 16.

Wiktionary
surnaming

vb. (present participle of surname English)