Only members of the list can send an email to the list - since the list names are tied to the sender's address you don't need to worry about uniqueness (ie. my family@fiesta.cc is different than your family@fiesta.cc)
when somebody tries to add you to the second one it'll be automatically renamed (just for you, not for everybody else) to family1@fiesta.cc - you can then go into the web UI and rename both however you want!