We know by hand for two possible ways of how someone can identify himself as the owner of a vault in Gringotts.
The first one we know of, from the HP & PS were Harry goes to Gringotts with Hagrid and the second is giving Harry's vault key to the goblin.
Also, on the same scene we can see that another type of identification is with a "letter" (I am talking about the letter that Dumbledore gave to Hagrid in order him to extract the Philosopher's Stone) but I guess because it was Dumbledore asking that it was a "special" case and that wouldn't happen with normal people.
The third one we know is from HP & DH I-II at which point Harry, Ron & Hermione are going to Gringotts after using the Polyjuice potion and Hermione has the form of Bellatrix and the identification is being done by Bellatrix's wand.
What other known ways do we know of for "customers" identifying themselves to the Goblins in order to get access to their vaults?