I think that when this happens with someone you know, all legal options should be explored as it can turn into a dangerous situation.
It happens with strangers as well, but this is why it is important to keep your personally identifying information off of sites like gransnet. If you use more traditional social media (FB, IG etc), educate yourself on the app’s privacy settings and adjust your profile accordingly. You can always report suspicious behavior to the app/site’s administrators, but results will be hit or miss. Unfortunately you’ll likely end up having to block the person each time. I’d still report each time.
When a person feels the need to create multiple accounts in order to harass a someone online, that individual has serious mental health issues. There is no telling what else they are capable of.