You can leave your stuff in the guest houses and hotels where you will be staying in Kathmandu. These guesthouses have a unique service designed for trekkers who need to store their belongings while they go on a trek in the Himalayas.
You can ask the caretaker to handle your backpack with care and also put up a large and visible name tag on the bags to avoid misplacement. The guesthouses readily agree to store your stuff as they can serve you further after your return from the trek.