Nonna is the Italian word for grandmother. Nonnina is a term of endearment meaning "little grandmother." Occasionally, nonnina will be shortened to nonni, but nonni is also the word for grandparents plural.
Nonna does not make the list of the most popular grandmother names, but many grandmothers who are not Italian have chosen it because it is short, easy for kids to pronounce and sounds good when combined with a first name.
Pronunciation: Go here to hear Nonna pronounced.