A useful book on this subject is available: 'Little Italy: A History of Liverpool's Italian Community' by Terry Cooke (copy in the AIFHS library, also available to buy, price £7.99 plus £2 p and p to UK mainland; link here for an order form (pdf 63kb) to order directly from the society and pay by cheque.
Terry Cooke points out that the Italians worshipped mainly at St Joseph's Church, Grosvenor Street, and Holy Cross Church, Great Crosshall Street and that Little Italy generally comprised Circus St, Gerard St, Hunter St, Lionel St, Whale St and part of Christian St, Clare St and Springfield St.
Terry Cooke has a page on the Scottie Press Website. Scottie Press is a Liverpool-based community newspaper for the Vauxhall area, with good coverage of the Italian heritage of the streets surrounding Scotland Road.
Some of the more prominent family names associated with this neighbourhood are recorded as:
The author notes that official records referring to the surnames of Italian immigrants show various spellings, many of which are only approximate, and that during the 1940s there was a tendency for the spelling and pronunciation of some Italian surnames to become anglicised. The names are reproduced as given in the book, but some of these are definitely unusual spellings of familiar surnames.