The rapid advancement of large language models (LLMs) has significantly improved their performance in code generation tasks. However, existing code benchmarks remain static, consisting of fixed datasets with predefined problems. This makes them vulnerable to memorization during training, where LLMs recall specific test cases instead of generalizing to new problems, leading to data contamination and unreliable evaluation results. To address these issues, we introduce DynaCode, a dynamic, complexity-aware benchmark that overcomes the limitations of static datasets. DynaCode evaluates LLMs systematically using a complexity-aware metric, incorporating both code complexity and call-graph structures. DynaCode achieves large-scale diversity, generating up to 189 million unique nested code problems across four distinct levels of code complexity, referred to as units, and 16 types of call graphs. Results on 12 latest LLMs show an average performance drop of 16.8% to 45.7% compared to MBPP+, a static code generation benchmark, with performance progressively decreasing as complexity increases. This demonstrates DynaCode's ability to effectively differentiate LLMs. Additionally, by leveraging call graphs, we gain insights into LLM behavior, particularly their preference for handling subfunction interactions within nested code.