Leveraging network information for predictive modeling has become widespread in many domains. Within the realm of referral and targeted marketing, influencer detection stands out as an area that could greatly benefit from the incorporation of dynamic network representation due to the ongoing development of customer-brand relationships. To elaborate this idea, we introduce INFLECT-DGNN, a new framework for INFLuencer prEdiCTion with Dynamic Graph Neural Networks that combines Graph Neural Networks (GNN) and Recurrent Neural Networks (RNN) with weighted loss functions, the Synthetic Minority Oversampling TEchnique (SMOTE) adapted for graph data, and a carefully crafted rolling-window strategy. To evaluate predictive performance, we utilize a unique corporate data set with networks of three cities and derive a profit-driven evaluation methodology for influencer prediction. Our results show how using RNN to encode temporal attributes alongside GNNs significantly improves predictive performance. We compare the results of various models to demonstrate the importance of capturing graph representation, temporal dependencies, and using a profit-driven methodology for evaluation.