In "The Giver", do the Birthmothers have a relationship with the same guy to have their babies?No
Although the mechanisms of impregnation used in the society are never detailed in the book, it would seem highly unlikely that the Birthmothers would engage in actual relationships with men in order to conceive. The sex drive in the Community has essentially been eliminated, with citizens required to accept treatment in the form of daily pills from the onset of puberty. When Jonas experiences the first vestiges of the sexual drive, or "stirrings", he must begin taking medication to suppress his desires, as does his friend Asher, and even his parents before him. Sexual relationships are not a part of the life of the people; connected as closely as they are with choice and emotion, it would appear that they would deviate too much from the requirements of regulation and "sameness" which govern everything that goes on in the Community.
Birthmothers bear three children within three years before they are assigned to be Laborers for the rest of their lives. They are essentially breeders, who bear their young according to the seasons. In keeping with the atmosphere of complete and sterile regimentation which rules every activity in the society, it would seem most likely that the Birthmothers' pregnancies are achieved through artificial means. That way, nothing is left to chance, or to human inconsistency. Everything is done according to a preordained timetable, orderly and predictably, and the government is in control.