Which saint gives New Year's Eve the name Silvester in several European languages?

Pope Sylvester I gives New Year’s Eve the name Silvester in several European languages.

Sylvester I was bishop of Rome from 314 until his death on 31 December 335. His feast day in Western Christianity is 31 December, so the date became associated with Saint Sylvester. In German-speaking countries, New Year’s Eve is commonly called Silvester; related forms are also used in several other European languages and regions.

His papacy fell during the reign of Constantine I, when Christianity was gaining legal recognition and major churches were being built in Rome. Sylvester’s pontificate coincided with the First Council of Nicaea in 325, although he did not personally attend; representatives were sent in his place. His historical biography is relatively sparse, and later traditions added legendary stories about his relationship with Constantine.

The name is sometimes written Sylvester and sometimes Silvester. That spelling difference reflects language and usage, not a different saint. The label refers to the pope’s feast day and death date, rather than to a special New Year doctrine he created.