I'd guess in most countries that follow the Name Day[1] tradition (most countries in Europe and Latin America, it appears), Sylvester's day is on Dec 31st[2]. The Germans just use the name to refer to the day (and spell it with an 'i' -- which TIL seems to be the original spelling); dunno, maybe others do too.

[1] https://en.wikipedia.org/wiki/Name_day

[2] https://en.wikipedia.org/wiki/Saint_Sylvester%27s_Day