Animals that use personal names
nautil.us
nautil.us
But hearing a person say "I am John Smith from Anytown, State, USA" would readily identify them and be a more similar comparison to the dolphin calls. If we take their assumption that there's no information content other than the sound, then sure, the comparison would be every John Smith singing a particular song.
Either way, that's just saying dolphins are better at hearing than us, which is less interesting.
Human names in an oral culture on the smaller family-and-friends scale seem like they'd be much more diverse, unique, and informal, with names that are more like nicknames than legal names. But certainly humans use them for gossip ;)
There's still a general rule to keep names unique within local groups, and it's weird to intentionally do otherwise (see Pete & Pete).
These animals might have "dialects" that only span a small number of individuals, so part of that "uniqueness" may just be dialect. I think you might see something similar in humans if you looked at small scale illiterate cultures in areas with a lot of linguistic diversity (e.g. Papua New Guinea)