Thanks  Avivah. The following may corroborate the point about the missing manifest. I include the details only to underscore how difficult it may be to ferret out family information once the older generation has gone.

 I finally went into the Hamburg passenger index through Familysearch, and looked for an 1879 departure to NY for a 5 year old boy born in 1874, and came up with the following for the Rinschek family departing on the Argo via Liverpool. https://tinyurl.com/y2zxangb

The demographic for Leib (Louis - born 1874, age 5 on departure) and Jakob (Joe - born 1868, age 8 at departure, close, not exact) work OK, as does the demo for Samuel (Simon - born 1845, age 34 on departure), but Jette is not a name that means anything and more important, the birth date (1849-1850) doesn't exactly correspond to our records. However, Miriam's gravestone says she was 80 at her death in 1927, which places her d/o/b at 1847, which isn't that far off, and as someone noted, most Jewish emigrants graduated from an entirely different calendar system, so its not surprising if this is inaccurate.

(Jette is Dutch or Nordic - hah! - but there is a Yiddish variant, Yutte, still not close to Miriam. Perhaps the shipping clerk  didn't get her name, and just assigned one arbitrarily.)

Unfortunately, there is no NYC manifest I could find for the Argo, or in fact for any arrival from Liverpool in 1879.  However, once the Rinschek family arrived in June of 1879, the name disappears. I can't find it in the 1892 state census or the city directory, or in any US census, which suggests the possibility that they simply abandoned the name once they arrived. Did they decide for some indecipherable reason to adopt a new name, and does the name suggest a point of geographic contact? And why abandon Samuel for Simon?

Unfortunately the town from which they emigrated - Schluzewa, Polen or perhaps Sluzewo -  is a long way away from Rzeszow and Przeclaw, where Miriam apparently lived. So, is it likely that Simon could have met Miriam at that distance, and if so, why her completely different given name at Hamburg?

I'm guessing this is a coincidence (unfortunately).

Alan Reische
Manchester NH