la réponse ici dans le dictionnaire berner
https://www.fhs.swiss/berner/?l=en
«
collet n.
Small split cylinder fitted frictiontight to the balance-staff. It has a small lateral perforation to take the inner end of the balance-spring, which is fixed to it by means of a pin.

A
Ferrule of a tool-handle. Metal ring v fitted to the end of a wooden handle to strengthen it.
Collar, collet. Small mobile ring fitted to mandrels and chucks to ensure their clamping action.

«
Je ne connais pas le nom en français, mais les horlogers du forum vont nous éclairer