Helmut, as always when you tell me something, I am totally astonished at the extent of your knowledge!!!
The source for the record transcripts I'm using is the LitvakSIG, which is part of jewishgen.org. What I see there are Latin alphabet, English language records (for which I'm very grateful!). The first names seem to be predominantly Yiddish, but sometimes nicknames and occasionally Hebrew names (using the name translator tool I mentioned, which is also on the LitvakSIG website). Rarely, they are Americanized names. Spelling of these names is all over the place, too, in different records.
For example, here is what I have found on different records (birth, marriage, death for him, his wife, and his children) for the first name of the person I entered as Sharia (Sokhen-2):
Sarje, Sarija, Sarijus, Sarjas, Sheria, Shaya, Shario
Most of them aren't this extreme, but this one isn't even in the translator tool, so I had no way to guess which name should be the "correct" one.
The East European Genealogical Society doesn't seem to be of any help with this (although it looks like another great place for me to look for information) and the other link is broken.
I guess it's a good thing that I'm only looking at pre-World War II records, so at least I don't have to cope with the mess the Nazis made of records! On the down side, it appears that the family has disappeared ... most either from Lithuanian or Russian persecution during the years between the Russian Revolution and World War II, and whatever small number survived that most likely did not survive the Holocaust. One of the historical background articles I read said that about 80% of Lithuanian Jews were gone before the Nazis ever arrived and over 90% of the remaining ones were killed between June and August of 1941.