This has come up before, so I'm rephrasing another poster's solid response to the question:
Sinjin is actually an attempt to represent phonetically the now rare name "St. John." As a given-name, "St. John" is sometimes pronounced as [SIN-jin] or [SIN-jun] in the UK. I presume this to be a relic of Norman-French origin (see also Sinclair for St. Claire).
Its spelling is not set in stone, I believe the forms Sinjin, Sinjun and Sinjon have been found.
The name has no 'meaning' in and of itself, but its usage is typically in honor of St. John the Baptist or St. John the Evangelist.
Now I mention just for hilarity's sake, if you've ever seen "A View To A Kill," one of James Bond's aliases is 'St. John Smith.' When someone calls him [SAYNT-jon SMITH] he corrects with the riotously English pronunciation [Sin-jin SMYTHE].