End-to-end autonomous driving (E2E-AD) has achieved remarkable progress. However, one practical and useful function has been long overlooked: users may wish to customize the desired speed of the policy or specify whether to allow the autonomous vehicle to overtake. To bridge this gap, we present Bench2Drive-Speed, a benchmark with metrics, dataset, and baselines for desired-speed conditioned autonomous driving. We introduce explicit inputs of users' desired target-speed and overtake/follow instructions to driving policy models. We design quantitative metrics, including Speed-Adherence Score and Overtake Score, to measure how faithfully policies follow user specifications, while remaining compatible with standard autonomous driving metrics. To enable training of speed-conditioned policies, one approach is to collect expert demonstrations that strictly follow speed requirements, an expensive and unscalable process in the real world. An alternative is to adapt existing regular driving data by treating the speed observed in future frames as the target speed for training. To investigate this, we construct CustomizedSpeedDataset, composed of 2,100 clips annotated with experts demonstrations, enabling systematic investigation of supervision strategies. Our experiments show that, under proper re-annotation, models trained on regular driving data perform comparably to on expert demonstrations, suggesting that speed supervision can be introduced without additional complex real-world data collection. Furthermore, we find that while target-speed following can be achieved without degrading regular driving performance, executing overtaking commands remains challenging due to the inherent difficulty of interactive behaviors. All code, datasets and baselines are available at https://github.com/Thinklab-SJTU/Bench2Drive-Speed