Yes. When you collect an e-signature, the driver can record who signed — the "Signed for" name is stored with the stop and appears in exports. For an explicit record, add a Driver Task text field for the recipient's name, and the driver can add a note or photo as well.
All of it is saved to the stop's proof-of-delivery timeline and can be shown on the customer's tracking page. Works in both EasyRoutes for Shopify and EasyRoutes for Web.
See: Proof of Delivery · Driver Tasks