The respect given to a drivers license as positive identification is quite surprising, even though to a large extent, it is not warranted. As an evidence of identity, a driver's license is as solid as water balloon. Yet, everyone continues to use and accept it as proof of positive identification.
The drivers license is almost universally demanded when cashing checks, which is why check artists always have a drivers license ready at all times. If you walk to a liquor store with a passport to purchase with a check, chances are you will be turned down in favor of the drivers license, even though passports contain more thorough information and are more expensive and harder to obtain than a drivers license.
It is with good reason why drivers licenses carry so much weight as proof of positive identification. In most states a drivers license is the only thing a person carries in the way of identification that has his photograph on it. In fact with some states, DLs also use thumb print, although the average store clerk cannot really verify that it is that of the user.
Although a thumb print is a far better method of establishing an identity than a photograph, for the shopkeeper who doesn't have the expertise to compare prints, the photograph is the best basis for accepting check payments. In fact, the drivers license is such a popular piece of ID that many states issue licenses even to people who do not drive. While it really isn't a "license" at all, since it doesn't permit the holder to do anything, it is useful and readily accepted as a form of personal identification.
Getting a drivers license late in life is quite common, it is not unusual for someone to walk into a DMV office and get a license for the first time. This is why a DL is something people get when they want to change the identity.
When asked why someone is getting a DL so late in life, a person changing identity can come up with a number of excuses. Many people don't have the money to buy a car until they've saved enough over the years. Another very rational explanation is that you've been living in a city with excellent mass transit and you did not have to drive.
When applying for your DL, bring your birth certificate or passport. Along with your other identifications, you will want to bring a few letters addressed to you as proof of your residence. It should be easy enough to arrange for them to show your mail drop address rather than your actual residence.