The phrase "one's own desk" means having a specific desk that belongs to oneself. It implies having a designated space where you work or study. Full definition
There is a 24 - hour front desk at the property. (hostelbookers.com)
I remember before they went to school, those three big kids sitting at desks at this blessed moment: those three kids came to us in four and a half years. (sarahbessey.com)
The bookshelf and pages open on desk in front of you.... (housegoeshome.com)