The Shakespeareans are a local gang in Venice, Newport. They seem to be cut from the same cloth as Warren Hughes' old outfit, the Razorblades on Hope Street. According to the Chinaman, a lot of kids in Newport are joining gangs because they think it's the only way to survive, but gang warfare means a lot of them get killed.
Zoë Castillo runs into a prospective member on the Venice Bridges who seems to be about Warren's age (13 in TLJ), but he threatens her off, telling her he's going to be earning his "name" soon. It seems that upon initiation, members take the name of characters from Shakespeare's plays. Their current leader goes by the name of Othello.
The gang seem to have taken their name given Shakespeare's affinity for the real Venice in Italy, which features in several of his plays.