Does the etymology of this name have any relationship to the English/Latin etymology of the word?
There are at least two saints, both of them are recognized by the Russian Orthodox Church. One is мученик (martyr) Модест, the other one is святитель Модест. It never was very popular in Russia but earlier, like in 19th century, it definitely was at least more popular than now.
Also, it actually was used more in Polish-Russian families rather than in families without Polish/Polish Jewish roots.