she told her name though, so her actually being there too is just a matter of plot convenience
and ultimately, this is a reign of terror - they wouldn't really care whether she lies or not, the results would likely be roughly the same. This kind of environment where it is more beneficial to rat on others (false or not) before they do the same is not uncommon in fiction and not without examples in real history either
the fact that people tend to crack and tell the truth under extreme pressure (in hopes of survival) plays into the hands of the oppression
It's not that she told the truth, is that the police immediately executes her and arrest the person she pointed to and call it a day.
It'd be another layer of plot convenience if we are to accept:
1. The police knows everybody in the town by name, so girl friend can't make up a random name, and Nona cannot feign ignorance like "who me?"
2. If the girl friend were to name another person who exists in the town, the police would've gone to their house and arrest them.
3. If the police executes her THEN find out she lied, now there's still a witch out there and you just ended your only lead. Reign of terror sure, but utterly ineffectual in smoking out witches if killing your lead without confirming is their approach.
If girl friend simply lied and got executed and Nona stayed home that day. The police will likely hang their corpses in town square to make sure the witch sees it so they can force the witches to try to leave town in the coming days and ambush them that way. If Nona and mom stays put and don't do anything (cast a spell to forget they ever know girl friend), then it could be years before the police get wind of their next slip up. How serious a threat are the witches if you can afford to be this laissez-faire with catching them and just letting them live amongst you.
All that is to say, the way they portrayed how they hunt witches in this town, it seemed girl friend was inexplicably given a silver bullet to take down anybody she accuse of to the grave with her. Townfolks at the scene ought to take note and react accordingly for when their time comes.