The presentation of a robot's capability and identity directly influences a human collaborator's perception and implicit trust in the robot. Unlike humans, a physical robot can simultaneously present different identities and have them reside and control different parts of the robot. This paper presents a novel study that investigates how users perceive a robot where different robot control domains (head and gripper) are presented as independent robots. We conducted a mixed design study where participants experienced one of three presentations: a single robot, two agents with shared full control (co-embodiment), or two agents with split control across robot control domains (split-embodiment). Participants underwent three distinct tasks -- a mundane data entry task where the robot provides motivational support, an individual sorting task with isolated robot failures, and a collaborative arrangement task where the robot causes a failure that directly affects the human participant. Participants perceived the robot as residing in the different control domains and were able to associate robot failure with different identities. This work signals how future robots can leverage different embodiment configurations to obtain the benefit of multiple robots within a single body.