@Highfivemum may I ask, do you some sort of local WhatsApp group or social media group? Because personally I would address this head on and would say I have no idea who this individual is, I met my DH at this school, we are 4 years different to the last in question and she has me mistaken for someone else. Do you have access to old class or school photos? Because I would quite literally take copies to her door and post them warning her to stop of you will seek legal advice as she is slandering you and threatening behaviour. I would also see if Police know her for having form for this unhinged behaviour. Who moves to an area and behaves like this?
I sympathize because in 2007 DH and I moved to a totally new area, 3 hours from my home town. I'd been there once to meet DHs family but never before that.
In 2009, I joined a mums group with the DCs and a lady there said she thought my face was familiar. I said it was doubtful unless she was from my hometown, she wasn't.
She then told another mum she knew me from school, at sixth form and apparently I was known as a right slapper and had eventually gone to prison for drug dealing.
It was utterly ridiculous and she wouldn't have even been in my year group. I collared her on it and told her in front of the rest of the mums that she better apologise and admit she was wrong or I would ask the group owner to remove her. She tried to wiggle out of it that I "definitely" looked like the person. It didn't matter there name was entirely different either.
That was sorted after that. Bullies like that need to be told, not aggressively, but forcefully. Stand your ground. And so walk your dogs as normal but film her if she does it again.