ZMP Controller described a clearance event when two company aircraft were on the reporter's frequency; one improperly. When the prior sector had assigned a frequency change; both aircraft took it.

Narrative

Working Sector 11; I took the hand off on Aircraft Y climbing from low altitude Sector 9 into my high altitude Sector 11. Aircraft Y was out of about FL190; climbing to 230. The data block indicated FL340; as per letter of agreement. A company aircraft checked on. I climbed it to FL340; which it read back. A few seconds later; Aircraft Y checked on; again; with a different voice; climbing out of FL190 to 230. I issued FL340 again; and thought about it. I quick-looked Sector 9; and saw that they were much busier than I was. Moreover; they had a Company Aircraft X climbing out of FL205; with FL340 in the data block; southbound towards Sector 18. On a hunch I asked if Aircraft X was also on my frequency. They were; and it was the voice of the first company aircraft. I immediately told them to maintain FL230 'only'; and to return to their previous frequency. They read it back and left my frequency. At no time did Aircraft X violate another controller's airspace. But it could have. Recommendation; I'm not sure. We all need to listen harder; I suppose.