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I have read where all Katznelson's are related, even though there are variations on the name: Katznelson, Katznelson, Katzenelson, Katsenelson, Katzenelnbogen, Katzenelenbogenson, etc. If true, we are therefore related to Berl Katznelson, one of the founders of the State of Israeli and of the Israeli Labour Party.
At least one, Henry, shortened his family name to Nelson, and therefore all of his descendants were named Nelson. Perhaps others changed their name or had their name changed by immigration officials when they immigrated to the US.
Deb Katz adds: While most Katznelsons (and variants) may have in common that their paternal lineage traces ultimately to Katzenelnbogen, Bavaria...and like most Ashkenazi Jews, most Katznelsons will be related in some way by means of a zig-zagging between various male and female lineages, NOT ALL Katznelsons are related on the Katznelson paternal line. This has been proven by the genetics. (Contact me if you want more details on that, but for example, one genetic study [Paull et al] gave evidence that the Saul Wahl Katzenellenbogen male lineage is in the YDNA haplogroup J1-L858 and there is a significant Katsnelson lineage which part of a J2a cohanim branch (FGC4992). J1 and J2 split from each other about 28,000 years ago, although both were present in the BCE Levant as the Hebrew tribes formed.)