You say you've known her awhile, yet have zero mutual friends to ask what her name is?
If you somehow forgot her name after knowing her awhile, that probably means you two haven't spent a lot of time together, so it's perfectly fine just to admit that you never caught her name.
Just say something along the lines of "This is going to sound silly, but I never actually caught your name...". Have a laugh about how crazy it is, seeing as how long you've known each other, but admit you've never had the chance to find out much about her, but are looking forward to doing so.
If you want to get more elaborate, introducing her to a friend is a good idea. Have a mate come with you to the date. Have him (or her!) introduce themselves, and just casually say to your date that you were having coffee with them and they were keeping you company while you walked. She'll probably see through it, but conclude that your mate was just curious about what she looked like.
Alternatively, make a joke about doubting she's old enough to drink, and of seeing her ID. Another way is to bring up at some point how embarrassed you are by your driver's license photo (maybe talking about photography, hating tests, hate posing for photo's ect). However, she can only see it if she shows you hers.