Sharing a living space with others (a Wohngemeinschaft or "WG") is very common in Germany. A number of students choose to rent a space privately in the city, usually in groups of two, three, or four, in which every person has her or his own bedroom, and in which the kitchen and bathroom are used commonly by everyone in the WG. These rooms are usually unfurnished, but it is occasionally possible to find a furnished room for one semester as a sublet.
The "Studierendenwerk Rostock" operates and maintains student dorms in different parts of the city. Here you can rent a furnished room for the duration of your studies.