Companions
Things were complicated. First, I wasn't sure it would work. I mean, did you see what I did to the TARDIS? The Lodestone was basically made of bits of TARDIS and gaffer tape. If sending you back didn't fix things, I'd have stayed on with UNIT, and Rose Tyler died in the Battle of Canary Wharf.
Two, who knew what you remembered about the Doctor? And when I traveled with him, he'd never mentioned anyone else from before. I'm actually surprised that he did say anything to you. Like, really really surprised. He usually just moves on, next planet, next companion.
Anyway, Bad Wolf is me. It's the name I chose for myself, and it's the reason my first Doctor regenerated.