Any available info we can share about the customer would be on your receipt. 

A customer’s name will be on the bottom-left corner of a payment receipt if this information is made available to Square from their payment card. For example, we're able to capture the name with our latest magstripe reader, so if you were using an older device at the time, or manually entered the sale, the name wouldn't have been captured!

Receipts can be found in the Transactions page of your online Square Dashboard. Hopefully that info helps!