The gagging sound may mean that he has Kennel Cough or he may just be getting used to his new environment...the new smells, the carpet, the dust, ect. Just ask your vet about it 2morrow. If he does indeed have Kennel Cough, your vet will give you some antibiotics for it.
As for naming him, I love the name PEEWEE! I think it is such a cute name for a cute itty bitty yorkie!!!!