Everytime I format a memory card the camera starts naming the images again from 0. This creates a lot of duplicate filenames which Lightroom thinks are duplicate images. I've unchecked the "Don’t Import Suspected Duplicates", but it still won't let me import those images.
Lightroom recognizes duplicates when they have the same original name, capture date/time, and file size.
In your case, the capture times should be different.
Is LR doing the copying of the files from the memory card? If yes, what folder are they going to?
but it still won't let me import those images.
You haven't convinced me the problem is the file name.
Exactly what happens when you try to import? If there is an error message, please quote the complete unedited verbatim word-for-word error message.
Also please state what version of Lightroom you are using, what camera took these photos, and are the photos JPG or RAW?