Is 嚘 commonly used in modern Chinese?

No, this is a rare literary character mainly found in classical texts and poetry.

What are the main contexts where 嚘 appears?

Primarily in classical Chinese literature describing sighs, sobs, or mournful natural sounds like wind.

Generally not recommended for names due to its sorrowful meaning, though it might appear in artistic or literary pen names.

嚘Tone 1

yōu ｜ 18 strokes ｜ radical:

To sigh;

to make a mournful sound;

to sob;

also refers to the sound of wind or other mournful noises.

To sighto make a mournful soundto sob

Deep sighMournful soundSobbing soundWind moaningLow sobSighing sound

This character appears in classical Chinese literature to describe mournful sounds and sighs.
It is considered a literary character and is rarely used in modern everyday language.
The character conveys a sense of melancholy and deep emotion in poetic contexts.