The only way I found to get both the item and customer's name is as follows:

1. Navigate to the Transactions page.
2. Set the date range to whatever dates you want to report on.
3. Click on the last option box at the top of the page (it probably says Card #) and check Item.
4. This is where it gets a bit squirelly: you'll need to enter the name (not SKU or other common identifier) of the item.  It doesn't have to be the complete name, but it should be enough that it specifies that item and no other, e.g. 'Shirt, blue' instead of 'Shirt', or 'Shirt, b'.
5. You'll get a listing of each sale of that item that was sold in the date range you specified, but no customer name (so you can't print from this screen by right clicking.)
6. Click on Export in the top right-hand corner of the screen.
7. Click on Transactions CSV and Square will export all of the information concerning the sales of that item, including the customer's name. (there's a ton of information included, so you'll need to weed it down to make it readable.)
8. Open the downloaded file with your favorite spreadsheet program.

Note, if you want to do all of your items at once, then filter them using the spreadsheet program, skip steps 3 and 4, and you'll get a report with every item sold during the specified time period.  You can then filter them based on Item Name in your spreadsheet program so they'll all be grouped together.