Brian Michael Bendis decided the Red Robin name Tim Drake was using was bad, and admittedly it is. His solution was to change it to…Drake. As in his last name. As in the duck. Supposedly a dangerous bird. If you’re a piece of bread maybe. It’s amazing that someone’s solution to a bad name…was an even worse name.
And yes, Batman is unshaven. Modern Batman is always unshaven even if Bruce is clean-shaven. It’s like putting on the cowl these days makes the stubble grow. It’s a strange, useless bit of magic.