Place the ham in a food processor and pulse 6-8 times, until finely chopped; being careful not to overprocess.
Transfer to a bowl and add the mayonnaise, dill pickles, pickle relish, onion, mustard, Worcestershire sauce, hot sauce, salt (ham may already be salty, so taste before adding salt), and pepper to taste; stir to combine.
Refrigerate until ready to use.
Can be used as a dip for crackers or spread on crostini.