According to various sources, Sylvester (also spelled Silvester) is named after Pope Sylvester I who supposedly baptized Constantine I on his deathbed or cured the late Roman Emperor of leprosy…the sources seem a little

confused on the specifics.  Pope Sylvester also seems to have ruled over the council of Nicaea (where a uniform Christian doctrine was canonized). It is also rumored that he was a pretty big anti-Semite, having pushed Constantine I to prohibit Jews from living in Jerusalem.  However from my recollection, Jews were prohibited from living in Jerusalem since the Bar Kokhba Rebellion ending in 135 CE, so perhaps that tid bit is not so accurate.

One thing that all the sources appear to agree on is that Pope Sylvester became Saint Sylvester after his death in 335 CE, and Germanic peoples have celebrated his death day around the end of December ever since.  Apparently, however, the original day was actually December 24th and was moved to December 31st after the introduction of the Gregorian calendar in 1582. 

The day has traditionally been commemorated in northern European countries such as Germany, Austria, Czech Republic, Germany, Poland, Slovenia…and, apparently, for some bizarre reason Israel.  None of the sources seem to provide a reason for why.

My instincts tell me that the Templers (Protestant community who settled in the Holy Land) brought Sylvester with them when they came to the region in the late 1860's.  Most likely people saw festivities (I bet they were rockin') occurring around the same time each year in the Templer quarters and eventually asked them what they were doing.  "Sylvester!" and a bottle of beer was their reply.