How to Index Multiple Documents in InDesign?

Marking up the InDesign documents to add all those names is in itself easy (with a script, as James mentioned). But the problem is that you won't be able to generate that index: InDesign can't open more than about 115 documents, and InDesign's index needs all documents open to create the index.

However, there are tools to create an index not using InDesign's index feature. The best one is 

https://indiscripts.com/post/2023/01/indexmatic3-what-s-new

Look into that script, it's probably the only way for you to create the index.

The first thing I want to say is that this sounds like a project that needs restructuring right from the start. Two hundred component files is... so problematic in so many ways. But let's just assume it's that way for a reason.

The only way to index that collection is using the Book feature, which I gather you understand and are using. So on a technical level, you're where you need to be.

As for adding all those names to an index list, and then generating that index... there are script solutions for some indexing tasks, and you can work from a list of index topics, but as far as I know these have to be set up and established (and even executed) on a file by file basis. That is, some 200 times. (Just one of the many reasons not to multiply components to this scale...) And 1,000 items in an index list is... a lot.

I think you're going to need some custom scripts, which may be outside what anyone, even here, is inclined to write and adapt for free. Or, I dunno, there are some wizards here who seem to have all such things already developed for sharing. But the short answer is that there is no simple, one-shot way to accomplish this task — there is no InDesign feature or other function you are overlooking, that is.

If it were possible, I'd start by consolidating these files into no more than about ten "chapters," and go from there. But you may not have that option, for functional or time reasons.