My experience is that there's a hybrid of different models. Some shelters think anonymity is the way that they should be presenting themselves in the community, while others don't do that at all. There are good reasons for both of those choices.
In my career, I have only twice had abusers show up at shelters looking for someone, with intent to harm them. For the most part, if a perpetrator is looking for the person they have victimized, they're generally going to do it in places where they're more likely to have access. There was recently a terrible case in Calgary where the perpetrator went to the school. That is one of the biggest risk places. Workplaces, schools and faith communities, I think, are the places where we most see perpetrators showing up with the intent to terrorize the victim.