Was the last name Skakun exclusively Jewish?

Hello!
No, the surname Skakun is not necessarily Jewish, but rather Cossack.
Name Hannah is also not necessarily Jewish, the Ukrainian and Belarusian form of this name is Ganna (Ãàííà), which is transliterated into English as Hanna. The same name in Russian is Anna.

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And was it common for those of Jewish ethnicity in the Russian Empire to have their children baptized in the Orthodox churches

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- yes, it was quite common. Conversion to Orthodoxy provided an opportunity to avoid restrictions on education and career prospects for Jews. If you interested in this topic, I recommend to read about: ×åðòà îñåäëîñòè, Êàíòîíèñòû, Âûêðåñòû
This article is about Jews in the Russian Empire https://arzamas.academy/materials/2203

Ôàìèëèÿ Ñêàêóí íå åâðåéñêàÿ. Áîëüøèíñòâî áåëîðóñû è óêðàèíöû. Ó ìåíÿ ðîäñòâåííèêè åñòü Ñêàêóíû - ó íèõ èç Áåëàðóñè ïðåäêè ïî ýòîé ëèíèè, íî èìåíà âñå ïðàâîñëàâíûå.
Ãàííà - ýòî èìÿ òîæå ó áåëîðóñîâ î÷åíü ðàñïðîñòðàíåíî, ó ìåíÿ â ðîäó ìíîãî ïî áåëîðóññêîé ëèíèè.

tIEWbTizk3xdUPYo íàïèñàë:

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Ukrainian.

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The archive translated the birth certificate into Ukrainian. The name, which is written "Àííà" in Russian, is written "Ãàííà" in Ukrainian. There is nothing Jewish in her first name, her last name, or the names of her parents.

ELM íàïèñàë:

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The surname Skakun is not Jewish. Most are Belarusians and Ukrainians. I have relatives named Skakun - their ancestors on this line are from Belarus, but their names are all Orthodox.
Ganna is also a very common name among Belarusians; I have a lot of Belarusians in my family.

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Áîëüøîå ñïàñèáî çà îòâåò. Ìîé òåñò ÄÍÊ ïîäòâåðäèë, ÷òî ÿ 100% âîñòî÷íûé ñëàâÿíèí, áåç åâðåéñêîé ãåíåòèêè.