Is 嚬 commonly used in modern Chinese?

No, 嚬 is primarily found in classical literature and poetry. In modern usage, 皱眉 or 蹙眉 are more common for 'to frown'.

What is the difference between 嚬 and 颦?

嚬 and 颦 are variant forms with the same meaning. 颦 is the more common traditional form, while 嚬 is an alternative character form.

Generally not recommended for modern names as it carries connotations of worry and distress. It's better suited for literary or artistic contexts.

嚬Tone 2

pín ｜ 19 strokes ｜ radical:

To frown;

to knit one's brows;

to scowl;

to grimace;

to express worry, displeasure, or deep thought through facial expression.

To frownto knit one's browsto scowl

To frownTo knit browsFrowning expressionFrowning and smilingFrowning in thoughtFrowning face

In classical Chinese literature, frowning (嚬) was often depicted as a sign of beauty, especially for women, where even their worried expressions were considered charming.
The character appears frequently in Tang and Song dynasty poetry to describe the delicate expressions of beauties or scholars deep in thought.
In traditional Chinese aesthetics, a slight frown could convey deeper emotional states than overt expressions, valued for its subtlety.