Oh, DB...she's a doll. And wonderful of you to adopt a "senior" dog.
I have no recommendations for names...I'm horrible at that stuff.
I know you'll come with something that suits her.
And extra cuddles to Bailey. Will the adoption agency provide help with bonding? I know with rabbits, they often benefit from going on a "bunnymoon" together - somewhere in neutral territory to make friends. Don't know if dogs are the same...