Are there sources for the etymology of the surname Katz being an acronym for Kohen Tzedek?
Is that simply a backronym?
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There are many manuscripts and early printed seforim in which this name appears and there is a " in between the kof and tzadi. This clearly indicates that it is an acronym. One source is the seforim of the Shach, in which, although he is commonly (currently) known by the last name Katz, he is called "Kohein Tzedek. Then look here. Notice that only 9 years later Kohein Tzedek has become Katz. The Salonika print is in Tav Kuf Samech Alef (5561 or 1801) and the Lvov print is in Tav Kuf Ayin (5570 or 1810.)
[This answer is adapted from my comments on this answer to another question. Thank you Ariel for the easy link!]
While Katz is likely an acronym for Kohen Tzedek, there is something else to keep in mind. Many names - especially those of immigrants - changed. This is especially true with immigrants to the US. This means that the name Katz could reasonably be a shortened version of something considerably longer, such as Katzenellenbogen, which is a place name (somewhere in Southern Germany near the Italian border). In that case, it has nothing to do with being a Kohen.
It would most likely be a backronym if all the Katz families were related. In fact there appear to be many distinct Katz families, and many (although not all) are cohanim, which implies that the name arose either independently or imitatively, perhaps at a time when Jews were obliged to take surnames by the secular authorities.
One interesting thing to note is that I have seen some records transcribe the letters כ"צ on a tombstone as if it were the name "Katz" - e.g., גרשן בן משה כ"צ becomes "Gershon ben Moshe Katz". If this occurred in secular records it would imply that some families may have adopted the surname Katz without really meaning to!
The Roshei Teivos of Cohen Tzedek is Kof Tzadi. My great grandfather was a Kohain and his last name was Kentof - which I was always told came from Kohain Tov.