Thankfully, Lightroom didn't allow me to copy files with the same name into the same folder.
Is there a way for me to batch rename the newer files?
Actually it is your operating system that prevents two files with the same name being in the same folder. Even when you force the issue. the operating system will append a "-1" on the second file with the same name going into a common folder. Since almost always the Images will have been shot on separate days this will not be a problem if you import into one of the LrC data named folder schemes.
I have lots of images with the same file name in my Lightroom Catalog and this has never been a problem. So it is really not an issue.
Even with the same camera you will not run into this issue if you set the camera naming scheme to not start over each time a new cars is inserted. Then the number suffix will accummulat up to 10,000 images before starting over.
There are some things you can do in the camera settings to minimise the issue In my experience, Nikons, Pentax and Fuji all allow you to manipulate the first 4 characters of the File name. If you do this you can create a unique 4 character file name prefix for each camer and not have duplication between camera. This is what I have done with the Pentax, and Nikon camera that I have owned over the last 17 years.
Many prople. choose to rename images on import in Lightroom. It is not really necessary since the naming conventions are of benefit outside of Lightroom and are only of benefit for unmanaged images where you need to read the file name to have a clue as to its provenance . Lightroom does not care about file names as long are you are using the metadata in the file header to organise your images. I usually keep the Folder pane off in LrC because all of my organization is with Smart Collections based upon metadata like keywords and capture date and other useflu metadata like flags and labels.
If you really have the need to rename files, the same naming presets used with import are available in the library module. Just select a group of images and apply one of the file naming presets. If you do I would recommend retaining the file number suffix incase you need to restore one of the images from a backup made before the images were renamed.
A lot of people that rename use a name based upon the capture datestamp (YYYY-MM-DD-HH-MM-SS) found in the file header. Other features can be included like Camera Model (Nikon Z7) and File name Number suffix. To rename, there is a little icon to the right of the File name in the metadata panel. Clicking on this opens a dialog where you can choose your file naming preset or create a new one.