The Vehicular Named Data Networking (VNDN) facilitates effective communication between vehicles and roadside infrastructure in Intelligent Transportation Systems (ITS). However, ensuring reliable data transmission in VNDN is a big challenge in the high mobility environment due to the frequent changes in the vehicular network topology. Therefore, this paper presents an enhanced vehicle tracking and mobility prediction method using a Recursive Least Squares (RLS) estimation technique to improve the reliability of data delivery in VNDN. The proposed RLS-based approach collects real-time signal parameters, such as Received Signal Strength (RSS), Global Positioning System (GPS) coordinates, and the speed of a vehicle, and predicts the position of a vehicle. Tracking the vehicle position will enable the VNDN system to deliver the data packet to the consumer vehicle. Considering the proposed RLS-based estimation technique, the packet loss and data delivery ratio can be significantly reduced in the VNDN environment. The experimental results show that the proposed method improves the Quality of Service (QoS) parameters, such as interest satisfaction ratio (ISR), latency, and throughput, compared to the existing approaches. This work also establishes the foundation for advanced and reliable data-forwarding techniques essential for the evolution of connected and autonomous vehicles.