Materials with tunable thermal conductivity play a critical role in advanced thermal management, including building and vehicle heating and cooling, solar energy harvesting, and energy storage. 2D materials provide a platform for controlling heat transport via surface modification. Using density functional theory and the Boltzmann transport equation for phonons, we demonstrate the ability to tune thermal conductivity in a 2D material by adding and removing atoms: (1) although is even stiffer than graphene, its lattice thermal conductivity at 300 K is nearly ten times lower (482 W/mK); (2) by adding atoms, the formation of a more complex dumbbell structure results in more tortuous paths for phonons, but counterintuitively, the room-temperature thermal conductivity increases; (3) by removing atoms, the thermal conductivity at 300 K further reduces to 34 W/mK. Moreover, shows much lower thermal conductivity than the dumbbell structures at low temperature but much higher thermal conductivity at high temperature, rendering and its derivatives highly promising for various applications at ambient temperature. All these distinct behaviors are related to the localized out-of-plane phonon modes that rely on chemical bonding. Our work provides an intuitive understanding of how structure influences heat transport and demonstrates the possibility to control heat transport precisely via structural modification.