The organizers of the New Canaan Swap Shop say a name like ‘Take It or Leave It’ may have fit the facility better, since the Transfer Station passholders who can use it are free to either drop off items as donations, pick up free stuff or both. But the “Swap Shop” name has stuck and, since an official opening last week that followed a soft launch around Thanksgiving, “stuff has been moving,” according to Robin Bates Mason, president of Planet New Canaan. “Sometimes when stuff comes in, it goes out right away,” Bates Mason said on Wednesday morning as she and fellow volunteers arranged items for the Swap Shop’s operating hours of 9 a.m. to 1 p.m. Thursday through Saturday. “We had someone bring in a big bag of PlayStation games. One guy brought in a year-old flatscreen TV and literally 20 minutes later it was out the door.