The continuous implementation of new High Voltage Direct Current (HVDC) systems in the existing power system arises different challenges and opportunities. One important decision to be made by transmission systems operators is the control role assignment of the Interconnecting Power Converters (IPCs) conforming the HVDC system. The control role is understood as the converter operation both on the AC side (grid-following and grid-forming) and the DC side (grid-following and grid-forming). In general, the control role of these IPCs is static, i.e., changing the control role of the IPC is typically not considered in the power system operation. This paper considers the control role of the IPCs as dynamic, allowing the operators to have improved performance, stability enhancement, and flexibility. A methodology to optimally assign the control role of the IPC for a day-ahead scheduled generation and demand profile is proposed. This methodology considers (i) small-signal stability, (ii) system dynamic performance, and (iii) steady-state performance. Finally, an optimization problem is formulated to determine the best converter control role configuration to operate in the considered power flow scenarios. The proposed techniques are validated in a system with high renewable penetration and highly variable power flows.