I ordered a bunch of NFC tags from a Chinese supplier (I know, red flags) with the promise that they will serialize my tags as instructed so it will work w/ our software and
No, the anti-collision identifier (UID, "serial number") of genuine NTAG203 chips cannot be changed. That serial number is permanently burned in during the manufacturing process. However, there are tags available (typically from Chinese suppliers) that behave similar to MIFARE Ultralight (and derivates like NTAG203) and permit changing the UID using special commands.
Note that genuine NTAG203 chips never have duplicate UIDs. If manufactured by NXP, they always have unique IDs. So if you encountered duplicates, its likely that those are counterfeit tags.