In Japanese birds “naru” which is used for when a bell or other inanimate object makes a noise but that word isn’t used for human singing (which would be “utau”).
In Japanese the standard word for birds singing is 囀る saezuru but can be 鳴く naku (to chirp). As ThisOneGuy said, the word for (human) singing, 歌う utau, isn’t normally used for birds.
That’s a good question. I’ve done some research, and I can’t find a definitive answer. The oldest proven connection between birds and song I could find was the Hebrew word for nightingale, “Zamir”, which has the same root as “Zemer”, another word for song. The word, however, only dates back to the 13th Century, so I can’t tell you if biblical-era Jews thought birds sang.
(The word “Zamir” also appears in Song of Song 2 12, but it’s unclear whether it refers to birdsong, singing in general, or something else entirely.)
I’ve heard of the English surname “Birdsong”. I’ve heard of the German surname “Vogelsong”. “Fogelsang” is out there, too – maybe a German or Dutch dialectal form, or from one of the Scandinavian toungues?
A tangent question to the OPs might be whether there are similar surnames describing “bird song” outside of the Germanic languages?
EDIT: To start answering my own question, I found the uncommon French surnames Chandoiseau/Chantoiseau with this meaning.
The most common German version of this name is “Vogelsang”, and that is just an antiquated form of “Vogelgesang” which is the contemporary word for “birdsong”.
In Brussels I used to live in a quarter called “Chant d’oiseau”, which in Flemish is called Vogelzang. It was/is a nice residential quarter where even nightingales sang.