So, technically, as to what I have been told by the banks and what I teach to my students in Personal Finance:
What you've done on your signature card, for those of us old enough to remember those, or now on the electronic signature device, is what your legal signature is at the bank, and thus is what they place (or should place) on your check, and how you should sign your checks. The bank tellers should technically check your identity each time you receive any cash back, thus they are supposed to either check it against your signature card/device, or they can check it against your license with your picture and signature, to identify you, which may not necessarily match your bank signature. The DMV in each state may have different rules on how you have to sign your license.
When you open your checking account at the bank, and they ask for your license, it is simply proof of who you are and not necessarily your signature. They want to see that the name matches the face on a government issued I.D. For that matter, you could use your Passport to open a checking account, which some people may that live in a city and they do not own a car and have never gotten a drivers license. Also, in some states you can get a government issued I.D. other than a drivers license for proof of person, which many youth do here in Alaska for various reasons.
So to add to the list of advice, this is what I tell my students and what I need to actually do myself. On a separate piece of paper you should write all your accounts, their numbers, and the phone numbers. This should be kept in at least two secure places. One, that you can come home to and immediately call all numbers if need be to cancel/freeze accounts, and another place, son/daughter/etc, who can be contacted to do the same thing if something happens for example while you are traveling, your secure copy gets destroyed by some awful chance, etc. You get the picture.
Anyways, that is what my two cents is. Hope this helps rather than muddies things.
Steven Alaska, who is dealing with a clogged/frozen drainage system that is backing up in the downstairs tub/garage and waiting for the plumber tomorrow morning.
amy in CNY (who is up at 3 a.m.....and doesn't know why...)