That is one example, I am talking about the animals humans think about when they think animal language: dogs, horses, cats etc.

Maybe some animals have language closer to humans, but it is far from the common definition for "animal language".

Say what you mean and people will understand. If you make a broad and generic claim and someone finds "one example" then there was a problem with your claim.

Have you never met a dog that knew it's own name? Or that developed specific signs to communicate it's needs with it's owner, like scratching at the door, barking at their food dish, etc? Do you think they were born knowing any of that? Is there any doubt in your mind that they're communicating in their own idiolect?

Are you saying that domestic animals don’t have language, but wild animals might?

Quite the human-centric view of the animal world you have there