As I read the following paragraph out of the book Breakfast at Tiffany's on page 39,
She was still hugging the cat. "Poor slob," she said, tickling his head, "poor slob without a name." "It's a little inconvenient, his not having a name. But I haven't any right to give him one: he'll have to wait until he belongs to somebody."
I can understand the meaning of the bold sentence, but I can not fully understand the usage of 'his'. From what I have searched, the meaning of his is this:
pronoun 1. the possessive form of he1. (used as an attributive or predicative adjective): His coat is the brown one. This brown coat is his. Do you mind his speaking first? 2. that or those belonging to him: His was the cleverest remark of all. I borrowed a tie of his.
It seems that the second meaning is the possible explanation, and from the sample sentences, I think 'his' here can be replaced by 'He' and 'him', is that right?
What is the grammar rule for this usage of 'his'?