John/Jack and Kate are just very common names for characters. Kate in particular seems to be a favorite action heroine name, probably because it is widespread and not particularly in or out of fashion as to make the character seem dated, but at the same time is not overtly feminine. It's also short for a more feminine name (Katherine or one of its many variations, including more trendy/modern ones like Caitlyn or old-fashioned ones like Kathleen), and with its predominantly hard sounds, can pass as the kind of nickname a tough, tomboy who grows up to be a detective would go by (and her grizzled but doting father can always call her "Katie" to show that she's a daddy's girl). "Mary" or "Ann" or "Jane" are more generic, but also more classicly feminine and associated with more typical female roles. Kate is one of those names that makes it clear she's a girl, but can still be tough or hang with the boys.