While the soup itself has a long history and is popular in many Eastern European countries, including Russia and Ukraine, the word "borscht" itself is thought to have originated from the Ukrainian word "борщ" (pronounced "borshch").
It's important to note that while Yiddish and Russian have their own words for the soup (in Yiddish it's "בורשט" (borsht) and in Russian it's "борщ" (borshch)), the English word "borscht" is ultimately derived from the Ukrainian word.