For my suggestions I've included variations of the same name, names that rhyme with or sound similar to that name, have the same ending or beginning as the name, or has a very similar feel to that name.
Charlie -- Charles, Carlisle, Carlow, Carl, Chuck, Carlin, Carlton, Charleston, Archie, Harley, Chauncy, Chaz, Chet.
William -- Will, Bill, Billy, Liam, Willem, Guillaume, Wilson, Willis, Maximiliian, Wilfred, Killian/Cillian, Gilbert, Ville, Wilhelm, Wilmer, Willard, Graham, Warren.
Henry -- Hank, Henri, Huck, Enrique, Hardy, Harvey, Harry, Emery, Hunter, Hurley, Harley, Omri, Emmett, Jeffrey, Geoffrey, Benjamin.
Samuel -- Sam, Samson, Simon, Simeon, Bram, Sean, Adam, Dan, Daniel, James, Emanuel/Emmanuel, Abram, Shane
Edward -- Eddie, Edmund, Ted, Theodore, Ward, Edison, Edgar, Edwin, Millard, Maynard, Elwood, Ford, Richard, Gerard, Bernard, Eamon.
Oliver -- Olivier, Orville, Collier, Donovan, Dorian, Alistair, Alvin, River, Oscar/Oskar, Ovid, Everett.
Sebastian -- Bastian/Bastien, Severus, Septimus, Severin, Seven, Fabian, Caspian, Cassius, Finian, Tristram, Tristan, Sylvan, Basil.