How do Ukrainian surnames work?

So I’ve been trying to research and learn a bit more about Ukrainian culture and stuff for funsies. I’m just wondering how Ukrainian surnames work. I searched it up and most of the results were that it’s patronymic and the wife gets the husband’s surname and she may have a feminine suffix (Zelenskyy, Zelenska) and that also applies to the kids ( daughter is Zelenka, son is Zelenskyy) but I find out it’s different for certain surnames and they might not have the added suffix? I’m a bit confused on this (or if my research was just plain wrong) so if any Ukrainians in the comments can educate me n this topic, that would be greatly appreciated.