You can change or edit the name of that card. It's just the name or nickname you gave it when you first swiped the card.

Tap the card to open it

Tap the Pencil/Pad icon in the upper right hand corner to edit the card. 

Change the name, add any other information such as the security code or issuer phone number, (did you know you could dial the issuer from here?)

Tap Save.

Next question might be, do you have to enter the security code? And the answer is no, it's up to you. It's useful if you want to Flip your Card in the app to show a store clerk. Seeing your signature there and your security code, just as a regular credit card would appear, will impress them!