I'm not left handed
No character has an offhand unless they are TWFing. If and only if a character is utilizing the Two Weapon Fighting rules found in the Combat chapter of the PHB, does that character have an offhand. Otherwise, whichever hand they are using to make attacks, or even a non-handed attack, is always main hand. This goes normal for any character, mmonk or otherwise.
The reason for this is that there seems to be a lot of confusion with regards to the phrase in the monk class "There is no such thing as an offhand attack for a monk striking unarmed." This phrase is redundant, since without TWF, which isn't mentioned in that text, there is no such thing as an offhand attack for ANY character, unarmed or otherwise. The default state of being for any character is sans-offhand, and only when a character TWFs does that character gain an offhand attack with all of the mechanical benefits and penalties that apply. I believe that the text there was simply to clarify that even though a monk may strike with multiple surfaces of their body in any combination, they aren't TWFing, and thus aren't affected by the TWFing rules. It's a backwards way of saying it, but its a valid interpretation that leads to the most internal consistancy across the rules. Monks play by the exact same TWFing rules as everyone else, why should they be different?