Nonno is the Italian word for grandfather. Also in Italian it is common to add suffixes to grandparent names. Uccio denotes smallness or affection and is sometimes added to nonno to create nonnuccio. Nonnino is also a term of endearment meaning "little grandfather." Occasionally, nonnino will be shortened to nonni, but nonni is also the word for grandparents plural.
See also a comprehensive list of grandfather names.