In Illy select the the color (an object with the color) or even the whole design then hit Edit->Edit Colors->Recolor Artwork.
In the next menu there's a small pallet icon (usually under the word "none") click it and go to Color Books and select your Pantone book of choice.
After hitting okay new document swatches will be created with the colors it chose. Took me 15 years to learn about that.
PS much easier, eye drop the color, double click the swatch, click Color Libraries and select your Pantone book.