I am new to lightroom. I have 20000 photos on my pc hard drive stored by date and in some cases in sub folders.(backed up on Amazon Cloud). If I take a photo from my pc into lightroom to edit and then save it back in the folder it came from but with a different name?
Yes, you can do that. You would use the save function, and when the dialog appears to enable you to choose the destination you with choose the folder from which the image originated, and then assign the image a unique name. This would be a new copy of the image and it would be added to that folder. That new copy would then have to be imported or added back into Lightroom.
Why would you want to do this? Lightroom is a non-destructive editor. That means that all the edits are saved with the image, not by altering the image. If you need an edited copy for some reason, you can export that copy if and when you need it, and with the settings (file type, image size) that you need for that particular purpose. There is no need to save edited copies in general, let alone to import them again.
I totally agree. There really is no reason to have a copy of an image in Lightroom. Lightroom is a place to store master images along with the adjustments made to those master images. If a copy is needed for e-mail or to send to a lab to be printed or for other purposes then a copy can be made. After the copy has been utilized for its purpose it can be discarded. There is no need to clutter up Lightroom with a bunch of copies. If it is decided that the master copy needs to be modified then the copies have to be updated as well, and that makes no sense to me. The OP merely asked if it was possible, and it is. But it is really an exercise in futility in my opinion.