The names of companion animals could, from the outside, be seen as freely roving elements in the onomasticon. There are few or no legal restrictions on their given names, so, in theory, a dog, or a cat, could have any kind of word creation as a name. Dogs and other companion animals play a larger role as family members in many countries than ever before, something that possiblyhas an influence on their names. My major aim here is to establish, from a socio-onomastic viewpoint, whether animal owners in general take advantage of this apparent liberty, or whether they restrict themselves to using otherwise well-established name groups, e.g. anthroponyms or older zoonyms. The first part of the study is devoted to dog names. A large corpus of such names used in Sweden during the last decade is examined. The features of the most popular names given to dogs are studied and their relationship to popular baby names is discussed. This is combined with a study of dog names attested only once in the corpus. The results are supplemented with some findings on general attitudes to names of companion animals, taken from a recent questionnaire survey of animal names