Since the cup of sake goes around from the guest of honor to the host, from the host to the next guest and from the next guest to the host, this is called 'Chidori no sakazuki' (a sake cup going around in a meandering fashion).
盃が正客から亭主、亭主から次客、次客から亭主、と回ることから、これを「千鳥の盃」と称する。