This name
https://surnames.behindthename.com/name/borzecki/submittedis originated from the Romanian town of Borsec.
https://en.wikipedia.org/wiki/BorsecThe local native population is called szekler (inhabitant of Transylvania) and the first three characters mean wine in the language there. So Bor means wine and zeck stands for "sec" a meaning any town in Transylvania. The last character "i" stands for the noble who is owning that town or is originated from that town and having the nobble rank through his noble name.
Also very common name in Transylvania and Hungary as Borszéki.