I can batch change a number of photos with new capture dates, and Lightroom continues to show these new dates as expected. But when I attempt to import all these newly-dated photos to a new location, and simultaneously direct Lightroom to change each photo file name to match its new capture date, it frustratingly changes the file name to the original "date taken" that I thought I had changed. Windows itself shows that the "date taken" indeed has not changed, even though Lightroom continues to indicate "capture date" as the new corrected date. What is going on? Can Lightroom actually change the original photo-taken date, or does it simply change it's own proprietary note for the capture date? I suspect a complicating factor is that I am importing in two stages: Once to a location to change the original date taken, and then these imported to create the new file name from the date taken. I'm doing it this way because I don't trust Lightroom to do all the things I want and then add them to my thousands of photos all found in folders with names based on date shot. Thanks.
Lightroom does reliably write capture time to industry-standard metadata fields in photos. If you are indeed using the File > Import command a second time to re-import the photos after first importing them into LR, what's likely happening is that you're not telling LR to write the metadata changes back to the photos. There are two ways to do this: 1) Select all the photos and do Metadata > Save Metadata To File, or 2) Select the option Catalog Settings > Automatically Write Changes Into XMP.
If this does not fix the issue, then you'll need to provide more detail about the precise steps you're taking, with command names and options.
direct Lightroom to change each photo file name to match its new capture date
Stepping back, re-importing the photos back into LR isn't necessary to rename photos with their capture date -- use the Library > Rename Photos command.