
Her birth records:
https://www.familysearch.org/ark:/61903/3:1:33SQ-GB29-X9D?i=121&...
and
https://www.familysearch.org/ark:/61903/3:1:33SQ-GB29-BJW?i=665&...
show no middle name at birth. The register (first link above) shows the notation for the Nazis assigning the middle name Sara. That does not gurarntee that she had no middle name before that, but it makes your theory likely.
Almost definitely from the Nazis.
Ordinarily Jewish people didn't have middle names back then. Women often had a Yiddish or Hebrew name AND a German name but thesr were not used in conjunction with one another ,rather separately according to the social situation.
If someone turns up after 1938 with the middle name Sarah or Israel the default assumption is that this is wrong, and also being that they were in the wrong place at the wrong time probably also that they were murdered in Shoah .