Susan
"Grandfather?"
"What is it, my dear?"
"I suppose if I am to interact with humans I really should adopt a name so that I may fit in with them, don't you think?"
"Hmm? Yes, yes, I suppose you are right. What have you thought of?"
"Well, Grandfather, I read the book series you recommended as one of the Terran classics."
"And which would that be? The Lord of the Rings? The Lord Peter mysteries, perhaps?" His granddaughter shook her head, smiling. "Harry Potter? I give up, my dear, which one?"
"The Chronicles of Narnia."
"Ah, yes, wonderful series, that. We really must go and meet Jack sometime." The Time Lord chuckled to himself with delight at the thought.
"I've decided that while on Earth, I want to be called 'Susan.'"
"Susan? Why pick that name, my child? Hmm? She leaves Narnia and never comes back. Why not 'Lucy'? She makes me think much more of you."
"'Lucy' means 'light', so obviously that should be the name for the TARDIS; she's the wardrobe and she's Lucy."
The TARDIS hummed a little brighter.
"See, she likes that," Susan smiled.
"What have I told you, my dear? Hmm? The TARDIS is not alive; it is simply a machine."
"Sometimes you are silly." She gave him a peck on the cheek. "And don't worry, Grandfather, I'll never leave you. Not ever."