I have the same situation as OP. What is the process for obtaining a new study permit? Should I change my Designated Learning Institution (DLI) through my GCKey account and then return to Canada where the border officials will issue me a new study permit? Is this correct?A visa and a study permit are not related. As @bongoman said, a visa is only for travelling to Canada. The study permit is what allows your study here.
You need to get a study permit that is valid for the entire duration of your studies. Yes, leaving your studies midway will raise questions, but if you have a good reason, and you are going to a PhD program from a good university, you should be able to get a new study permit.