my cats do that too.a few of them will claim something and sleep with it or carry it around the house.
like my sam loves this toy and it really is 'his' toy.if he hears it...he perks right up and runs down or up to get it.
he even puts it in the water while he drinks it so noone will take it.

my lucy likes her green mousy...no other color.it has to be a green one.
and others have their certain toy that they like,or sock filled w/catnip.

it seems they all have different personalitys and like their own thing.just like yours