In the U.S., how are Ukrainian and Russian last names legally/generally feminized?

If my last name is Yaroslavskyy (or any other -skyy) according to the International pport issued by Ukraine, what is the last name spelling of my wife (who is an American) going to be? Yaroslavskaya? Yaroslavskyy? Yaroslavski? Up to us? Any foreseeable issues with Social Security Administration or other government agency in the States in relation to such name change?