The name and the Open button do the same thing: open that customer's record. Nothing on the list itself changes anything.
What you get
Their contact details and address, their order history, their store credit and loyalty ledgers with every movement on them, and their patron card. It is also the only place credit can be adjusted.
Getting there from elsewhere
You do not have to come through this list. The Customer panel on any order links straight to the same record, which is usually the faster route when you are already looking at the order somebody is ringing about.
Opening a record needs permission to view customers; adjusting credit is a separate permission on top. Staff can be given the ability to look somebody up without the ability to put money on their account. See Roles & permissions.