In-universe, all of the Officer Jenny's are indeed cousins. They merely happen to all look like each other, dress identically and work in the same profession. Ash puts this down to a strong family resemblance (warning, TV Trope links!)
Ash: Officer Jenny!
Jenny: Huh? Have we met before? Your face doesn't look familiar.
Ash: We met you back in Viridian City, remember?
Jenny: Oh, you mean one of the other Jennys. My cousins.
Jenny: My cousins are all police officers. All of us look identical plus we're all called Jenny.
[shows photo of nine identical Jenny's in police uniforms]
Ash: Talk about a family resemblance
Here Comes the Squirtle Squad
Interestingly, it would appear that the term 'Jenny' may be a family name, or possibly even a title since we meet at least one young Jenny in training (Marble) in Luxray Vision! that has a first name other than Jenny.
Marble: That's why Jenny Trainee Number One, me, came to investigate you!
Ash: You mean you're...
Dawn: [interrupting] Number one?
Marble: Right! ... The name's Marble, super-duper ace detective!
The name Joy appears to be a surname, rather than a forename. In Drifloon in the Wind we meet the daughters of an older Nurse Joy who plan to become Nurse Joys themselves. The family resemblance between mother and daughters is extremely striking.
Ash: You girls are so nice
Marnie: We're going to be 'Nurse Joys', just like mom!
Marnie: My name is Marnie Lynette Francis Joy
Peach: And I'm Paige Francis Lynette Joy.
Drifloon On the Wind!
Out of universe, it's worth noting that both 'Jenny' and 'Joy' are plays on the Japanese words for Constable (巡査 - junsa) and Female Doctor (女医 - joi)