Well, I like to build up emotions in a game - so if I had a herd of donkeys or scorpions = no closer emotions.
But if I have one and can name it, it becomes a pet. Something I want to take care of and protect, not only something I find useful. Same goes for giving this pet a name: I would shield it and maybe this donkey would even show an individual behaviour = kick me or bounce if it is overloaded - refuse to move on if it needs its sleep - stop following me and graze, if it's hungry.
These are the little things that add atmosphere to the game IMO and make me feel at "home" (in the sense DAD meant in another post)= identify myself with this RR world and want to play in it.
Addendum: Jurak, it was the griffin's name