It took its name from St Paul's, St Paul's Square, near Exchange Station.
Along with the Cunard Building, it was one of the few major buildings in Liverpool where building work was allowed to continue during the First World War.
(For instance work on St Philip Neri in Catharine Street was delayed so much that it didn't open until 1920.)
St Paul's opened in 1916 and had been designed by Giles Gilbert Scott while he was working on his masterpiece, the Anglican Cathedral.
I like St Paul's, especially for its very unusual design, which looks quite Continental to me.