Longman Dictionary of Contemporary English
second name
noun
EXAMPLES FROM CORPUS
▪ As a teenager he dropped his first name, Paul, and used only his second name, Jackson.
▪ I am afraid I don't know his second name, but I have been his friend since he was a boy.
▪ It had been Arthur's brainwave in the night; they must know Clare's second name, and address.
▪ It s your second name...
▪ Not even the second name, Al Gore, is likely to make much difference.
▪ Peter Catherwood finally snapped when the child referred to him by his second name.
▪ So I swapped Nigel for Oliver, which was always my second name.
▪ They will then supply the missing second name.
Wiktionary
second name
n. 1 surname 2 middle name, second forename
Wikipedia
Second Name
Second Name (El Segundo Nombre in Spanish) is a 2002 Spanish horror film. The film is based on 2001 horror novel Pact of the Fathers by English horror writer Ramsey Campbell.