Like many animals, parrots make sounds that suggest they are talking with each other, maybe even calling out to a specific parrot. But do they truly have names in the same way people do? To find out, Lauryn Benedict, a biology professor at the University of Northern Colorado, didn't set up shop in the tropics to record parrot chatter, as they've done in the past. She instead found birds who spoke her language—birds that live with humans and mimic what they hear, including people's names.
Isn’t there at least indications that corvids have an actual language, beyond just a set of specific calls? There have been indications they are able to transmit fairly complex information.
There’s some amazing info on crow communication here: part 1, part 2. Not actual language* yet, but it shows they’re doing far more than caw-ing at each other, and they do associate meaning with specific calls.
The first link even mentions crows raised by a human tend to repeat their names if they’re looking for the human; that’s really close to what the parrots do, it’s more like they have a name for the relationship than for themselves.
*so far the closest I’ve seen was cetaceans using some sort of phoneme equivalent, and chimps pairing vocalisations for subtler meaning (e.g. up+threat = flying predator).