DNA is unique.DNA "fingerprinting" actually has nothing to do with fingerprints. Since fingerprints have been used in American courts since the Jennings case in 1911, maybe they used the term "DNA fingerprint" to help people grasp the concept of comparing two samples side by side, trying to find similarities and differences between them.
Fingerprints are actually more unique than DNA. Identical twins (and other identical multiples) have identical DNA but different fingerprints. Every finger is different than every other finger in the entire world - including the other fingers on the same hand.