So, okay. In the Anime, Nurse Joy is one of a couple of NPC families, probably an in-joke about being based on an RPG. In the original series, they were all identical individuals who were related (through marriage inexplicably sometimes) who shared the same name.
Not only are they physically identical, but they also have regional variants, which honestly are just like clothing style and hairstyle differences as art changes aside, they still look similar enough between regions that a hairstyle change could make them pretty good ringers for one another.
But, then in Diamond Pearl, they delivered this shocker:
We met Marnie and Page Joy and their father, Karsten. The implication is that
1.) Nurse Joy genes are passed down matrilineally. Anybody can have a child with the Nurse Joy and there is a chance they'll be like a clone of the mother.
2.) Joy is in fact their last name and that too, is passed down matrilineally. Having a living father does not stop them from having the last name Joy.
Now, Horizons/Pokemon SV gives us a unique specimen. A teenage/young adult delinquent Nurse Joy. Now, the Mossui Town Pokemon Center Lady isn't CONFIRMED to be a Nurse Joy relative and as far as we know, there's no other nurses in her region that resemble her.
In the most recent Japanese episode, we also see a Grandma Joy, confirming in fact that Nurse Joy does age, but also she's a Kanto Nurse Joy with a unique hairstyle compared to even the Joys at the same Pokemon Center.
But, then there's Molly. Molly is the first Pokemon Nurse who's a main character. She's IMPLIED to be a Nurse Joy as she claims to come from a family of Pokemon Doctors and is seen eventually working for Pokemon Centers.
When she as a young Pokemon Doctor, she bore a passing resemblance to a Galarian Nurse Joy, but notably, has always had a distinct design from the identical Nurse Joy family, which grew more distinct when she became independent and decided to travel the world treating Pokemon rather than stay at a Pokemon Center.
However, despite being a distinct design, she shares the basic physical features of a Nurse Joy as well as the voice actor, implying some manner of relation.
