Is it possible for degu to have only one owner he minds, as a dog does?
It's possible to say 'yes'. Degus behave shy to people they don't know very well. If there are two people (like husband and wife) who both spend a lot of time with degus, they love them both but it seems that they usually prefer one of them more (thogh there is not much difference). But don't assume that degu will mind every word you say. They can understand people more than hamsters do, but not as much as a dog (or maybe they are too proud to do so :-)