Petri nets with name creation and management (-PNs) have been recently introduced as an expressive model for dynamic (distributed) systems, whose dynamics are determined not only by how tokens flow in the system, but also by the pure names they carry. On the one hand, this extension makes the resulting nets strictly more expressive than P/T nets: they can be exploited to capture a plethora of interesting systems, such as distributed systems enriched with channels and name passing, service interaction with correlation mechanisms, and resource-constrained workflow nets that explicitly account for process instances. On the other hand, fundamental properties like coverability, termination and boundedness are decidable for -PNs. In this work, we go one step beyond the verification of such general properties, and provide decidability and undecidability results of model checking -PNs against variants of first-order -calculus, recently proposed in the area of data-aware process analysis. While this model checking problem is undecidable in the general case, decidability can be obtained by considering different forms of boundedness, which still give raise to an infinite-state transition system. We then ground our framework to tackle the problem of soundness checking over workflow nets enriched with explicit process instances and resources. Notably, our decidability results are obtained via a translation to data-centric dynamic systems, a recently devised framework for the formal specification and verification of data-aware business processes working over full-fledged relational databases with constraints. In this light, our results contribute to the cross-fertilization between the area of formal methods for concurrent systems and that of foundations of data-aware processes, which has not been extensively investigated so far.