Each fingerprint must have a unique ID that refers to that fingerprint.
What you need next is a table to associate multiple fingerprint IDs with "persons" so that you can find out which person belongs to a particular print scan.
You didn't say if you were holding fingerprint and person data within the Arduino or on some network-based storage system, but if we assume that this is entirely self-contained in the Arduino you would need to write the association table to some kind of storage that won't reset when the Arduino loses power, such as an EEPROM. The Uno has a "built in" EEPROM on the ATMega328p chip, but it only holds 1024 bytes. There are external EEPROMs that communicate via SPI or I2C that can hold more data.
As to the actual data structure -- it can be as simple as a 2-dimensional array, with one dimension holding the fingerprint ID, and the other holding a person ID. For multiple fingerprints of the same person, the table would have multiple rows with the same person ID, but different fingerprint IDs.
You could also make an array of
struct datatypes, or create class, etc. But the point is that the "Unique ID" matching only ONE print from the fingerprint sensor is a limitation you have to work with.