I've read 2 different series of books, both that have a place named "Winterfell" that is central to the plot, but whilst reading the second series I no longer thought about the place in the first series after around 15 minutes. Readers will have different things called to mind depending on the context, and it will be unlikely that they are reminded of the previous location after a while.
However, even though there are over 30 locations in the US called Manchester alone, as well as further places with the same name in other countries, no matter how much I hear it my mind will always first jump to the place I grew up in the UK, because that's what I immediately think of when I hear the name.
So I think it really depends on whether the reader has enough attachment to something with the name already, but this could happen with names of anything. If a reader's sister is named Sarah, and the main character of the story has the same name, it may be very difficult to disassociate the character from their sister even if they are entirely different. There is absolutely no way a writer can accommodate for this.
But if, as you say, it's highly likely that your audience would have read a book not only with the same place name but having it as the title of that book, it may be better to err on the side of caution. After all, if you knew a large portion of your readers had a sister named Sarah, you'd probably give your main character a different name.
But generally, place names like the examples given in your question are named after something in the area that represents that place. But that means the founder could have named it slightly differently depending on how they saw it, but it would not have to be too dissimilar.
So rather than having the name Broken Rock it may have been named Rockfall, or Black River could be something as simple as Dark River. This could help with being very similar thematically, whilst also not being associated with a place the reader may already know of.