Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. But depending on the partial differential equation that one wants to solve, removing some important geometrical features may greatly impact the solution accuracy. For instance, in solid mechanics simulations, such features can be holes or fillets near stress concentration regions. Unfortunately, the effect of geometrical simplification on the accuracy of the problem solution is often neglected, or its evaluation is based on engineering expertise only due to the lack of reliable tools. It is therefore important to have a better understanding of the effect of geometrical model simplification, also called defeaturing, to improve our control on the simulation accuracy along the design and analysis phase. In this work, we consider the Poisson equation as a model problem, we focus on isogeometric discretizations, and we build an adaptive strategy that is twofold. Firstly, it performs standard mesh refinement in a (potentially trimmed multipatch) defeatured geometry described via truncated hierarchical B-splines. Secondly, it is also able to perform geometrical refinement, that is, to choose at each iteration step which geometrical feature is important to obtain an accurate solution. To drive this adaptive strategy, we introduce an a posteriori estimator of the energy error between the exact solution defined in the exact fully-featured geometry, and the numerical approximation of the solution defined in the defeatured geometry. The reliability of the estimator is proven for very general geometric configurations, and numerical experiments are performed to validate the presented theory and to illustrate the capabilities of the proposed adaptive strategy.