The proper pronunciation of Caligiuri is “Cal-i-gee-you-ree”. The emphasis is on the third syllable, and the “i” within the second syllable is pronounced with a brief “i” sound, as in “sit”.
Caligiuri is a standard Italian surname, and it’s also the title of an expert soccer participant who has performed for the US nationwide staff. The title is of Italian origin, and it means “shoemaker”.