“_1” follows file name after batch renaming

When I have bacthed rename the image files in a folder, then do an edit and remove a few images, I’d like to once again batch rename all of the remaining images so that the numbers are sequentially in order starting from number 0001, (example: “Anchorage 0001”). When I then do another batch rename using “Anchorage 0001” as the starting point, all the newly created files will have “_1” after the file name (“Anchorage 0001_1). This folder will also contain all the original files with their original file names. Is there a way to batch rename and replace all the original file names without the “_1” ending? Thank you for any help.