Numerous applications in 3D underwater sensor networks (UWSNs), such as pollution detection, disaster prevention, animal monitoring, navigation assistance, and submarines tracking, heavily rely on accurate localization techniques. However, due to the limited batteries of sensor nodes and the difficulty for energy harvesting in UWSNs, it is challenging to localize sensor nodes successfully within a short sensor node lifetime in an unspecified underwater environment. Therefore, we propose the Adaptive Energy-Efficient Localization Algorithm (Adaptive EELA) to enable energy-efficient node localization while adapting to the dynamic environment changes. Adaptive EELA takes a fuzzy game-theoretic approach, whereby the Stackelberg game is used to model the interactions among sensor and anchor nodes in UWSNs and employs the adaptive neuro-fuzzy method to set the appropriate utility functions. We prove that a socially optimal Stackelberg–Nash equilibrium is achieved in Adaptive EELA. Through extensive numerical simulations under various environmental scenarios, the evaluation results show that our proposed algorithm accomplishes a significant energy reduction, e.g., 66% lower compared to baselines, while achieving a desired performance level in terms of localization coverage, error, and delay.