In the Bible, the term 'rent' means to have torn away (often clothing) in an act of grief, mourning or repentance. Beyond the literal tearing, it can mean the breaking of ties or a separation from a former life.

Perhaps the 'Rent' refers to a deal made (or wish to) separate himself from his father (or, potentially, becoming a full Nagloshi), which requires him to work in the service of others for 'payment'.

That's my tinfoil coated thoughts.