Early naturalization records have very little information on them. Basically, what is on the index card is pretty much it.
Not to say that you shouldn't look for the actual papers. They can be rather humorous. I had one that went on for 6 pages on what a great guy he was without any genealogical information.
I have never seen a ship's name on any of the documents I've seen.
Secaucus NJ USA
HASSMAN, SONENTHAL, DAUERMAN, LUCHS - Drohobycz, Ukraine
HIRSCHHORN, GOLDSTEIN, BUCHWALD - Dolyna, Ukraine
ELLMAN, COIRA, MAIDMAN - Minkovtsy, Ukraine
KAGLE, FASS - Ulanow, Poland