As a descendant of Schwartz ancestors who is still looking for information about my great-grandfather's past, I took a keen interest in your question and the answers you received.
My experience is that names on passenger records more closely resembled the names used in the Pale and that the name change took place after arriving in the US (e.g., Schwartz recorded on the manifest and Black in Brooklyn). Your question seems to be assuming the reverse.
Also, I don't believe anyone literally "signed" their passenger record. As I understand it, the name on a manifest was written by a clerk from the information provided to the steamship company when the passage was arranged. Thus there was a certain amount of 2nd or 3rd party involvement in what was put down on the passenger record and plenty of room for error. (My ggm Dora Zarov shows up in a passenger record written as Barow.)
Tickets could have been purchased in a different name for reasons of ... let's say convenience. Say a family member already in the US who'd taken the name Black was listed as the party the passenger was joining. Or a blended or extended family traveling together. They may decide it's less confusing to immigration to say that your name was Black rather than Shmeggege than explaining why you are joining or traveling with family by the name Black. I've heard a lot of narratives about a "son" or "wife" listed on a manifest who actually turned out to be a nephew or a widowed sister whose actual name was different than what was recorded.
There is no hard-and-fast rule for name changes. Black indeed could be a straight-ahead translation of Schwartz but, as others have pointed out, there are variations such as Schwarzman and Schwarzstein, which complicate the search. My great-grandfather went by the name Joseph Schwartz but the earliest reliable record I can find for him is an 1897 NYC marriage record under the name Schwarzman. I haven't been able to find a passenger record for any Schwarzman that fits his profile. At the same time I have a lot of DNA matches with descendants of a Samuel Schwartzstein and I can find 2 passenger records for Jos. Schwarzstein which fit my great-grandfather. Schwartz, Schwarztein (with and without the extra T) and/or Schwarzman? I still don't know but it helps to be flexible.
BTW, family lore said that my great uncle Hyman Schwartz changed his name to J. Herman Black when he moved to Los Angeles. I wasted a lot of time looking for him under that name before eventually finding volumes of records for him – marriage, divorce, marriage, city directories, death and burial – under Herman J. Schwartz.
Also, as pointed out, there are means of naming or re-naming yourself other than translation. Black could have been the closest or most familiar rendering a similar sounding name. If you search "Black" in JewishGen's FamilyFinder the majority of entries are Block, but also Blauk and Black. I'd guess that Bloch might also be a contender. It helps that JRI-Poland and other search tools have a sound-alike search function which can help with those hurdles. I tried searching for JRI-Poland for the name Black and it retrieved almost 700 records, mostly under Bloch. In 1875, when your ggf made the crossing, Wroclaw was Breslau, Germany. https://beta.jri-poland.org/town/Wroclaw/
BTW, while the suggestion of Szymel is the common rendering of Samuel in Polish, there are no Szymels in among the records I found. Samuel is Samuel there. There are earlier Samuel Blochs in these records and, given Ashkenazi naming traditions, that can be a clue to finding earlier generations.
You may have more success learning your ggf's surname through other strategies or combining strategies. You don't mention whether the 1875 manifest records the name of someone in the US he was joining. If so, and if a family member, can be a useful clue. Look into manifests for any other family that joined him later. Other records in the US may provide other names: marriage and death records may provide parents' names (and a mother's maiden name may lead to a marriage record ...) You also don't mention what name your ggf used in the US. (The fact that you note how he was ID'd on the manifest suggests it was different.) Do you know where he is buried and do you know what is inscribed on his headstone (father's name and any additional information that can serve as clues about the family)? And as you build your family tree, pay attention to the more distant cousins who may be a link back to your ggf's birth family. Also, DNA matches, if you've tested, can point to previously unknown family connections which in turn can identify surnames and home towns.
Finally, if you are still stuck, it may help to know that this is a pretty common brick wall, trying to trace a family member before they immigrated. Name changes, sketchy records, missing records ... all are part of the rupture that is created by such historical moments as a mass migration.
Lee David Jaffe
Surnames / Towns: Jaffe / Suchowola, Poland ; Stein (Sztejnsapir) / Bialystok and Rajgrod, Poland ; Joroff (Jaroff, Zarov) / Chernigov, Ukraine ; Schwartz (Schwarzman?, Schwarzstein?) / ? ; Koshkin / Snovsk, Ukraine ; Rappoport / ? ; Braun / Wizajny, Suwalki, Poland, Ludwinowski / Wizajny, Suwalki, Poland